Your question seems to be equivalent to: why don't Democrats start acting like (small-government) Republicans when it comes to healthcare? Because that's not their idea of healthcare, or rather it's not what their electorate wants/expects:
(Some Democrats like Bill Curry even blame Obama for promising [in 2008] but eventually failing to deliver a federal public option with ACA.)
And, believe it or not, Sanders argues that Medicare for all would reduce administrative overhead:
There are certainly policies in the Sanders plan that would reduce American health care spending. For one, moving all Americans on to one health plan would reduce the administrative waste in our health care system in the long run.
And there is some data potentially backing up this
One 2003 article in the New England Journal of Medicine estimates that the United States spends twice as much on administrative costs as Canada. A 2011 study in the journal Health Affairs estimates American doctors spend four times as much dealing with insurance companies compared with Canada.
Warren's plan even promises a concrete figure for this cost reduction
$11 trillion in household expenses back in the pockets of American families.
But despite what politicians may be saying/proposing, there are few proven ways to substantially reduce healthcare costs (short of reducing care as well):
A new study, published Monday in JAMA, finds that roughly 20 percent to 25 percent of American health care spending is wasteful. It’s a startling number but not a new finding. What is surprising is how little we know about how to prevent it. [...]
Following the best available evidence, as reviewed in the study, would eliminate only one-quarter of the waste — reducing health spending by about 5 percent. [...]
The largest source of waste, according to the [2019 JAMA] study, is administrative costs, totaling $266 billion a year. This includes time and resources devoted to billing and reporting to insurers and public programs. Despite this high cost, the authors found no studies that evaluate approaches to reducing it.
“That doesn’t mean we have no ideas about how to reduce administrative costs,” said Don Berwick, a physician and senior fellow at the Institute for Healthcare Improvement and author of an editorial on the JAMA study.
Moving to a single-payer system, he suggested, would largely eliminate the vast administrative complexity required by attending to the payment and reporting requirements of various private payers and public programs. But doing so would run up against powerful stakeholders whose incomes derive from the status quo. “What stands in the way of reducing waste — especially administrative waste and out-of-control prices — is much more a lack of political will than a lack of ideas about how to do it.”
While the lead author works for Humana, he also has experience in government and academia, and this is being seen as a major attempt to refine previous studies of health care waste. Reflecting the study’s importance, JAMA published several accompanying editorials. A co-author of one editorial, Ashish Jha of the Harvard Global Health Institute and the Harvard T.H. Chan School of Public Health, said: “It’s perfectly possible to reduce administrative waste in a system with private insurance. In fact, Switzerland, the Netherlands and other countries with private payers have much lower administrative costs than we do. We should focus our energies on administrative simplification, not whether it’s in a single-payer system or not.”
After administrative costs, prices are the next largest area that the JAMA study identified as waste. The authors’ estimate for this is $231 billion to $241 billion per year, on prices that are higher than what would be expected in more competitive health care markets or if we imposed price controls common in many other countries. The study points to high brand drug prices as the major contributor. Although not explicitly raised in the study, consolidated hospital markets also contribute to higher prices.
A variety of approaches could push prices downward, but something might be lost in doing so. “High drug prices do motivate investment and innovation,” said Rachel Sachs, an associate professor of law at Washington University in St. Louis.
That doesn’t mean all innovation is good or worth the price. “It means we should be aware of how we reduce prices, taking into consideration which kinds of products and which populations it might affect,” she said.
Likewise, studies show that when hospitals are paid less, quality can degrade, even leading to higher mortality rates.
Other categories of waste examined by the JAMA study encompass inefficient, low-value and uncoordinated care. Together, these total at least $205 billion.
With more than half of medical treatments lacking solid evidence of effectiveness, it’s not surprising that these areas add up to a large total. They include things like hospital-acquired infections; use of high-cost services when lower-cost ones would suffice; low rates of preventive care; avoidable complications and avoidable hospital admissions and readmissions; and services that provide little to no benefit.
In addition to wasting money, these problems can have direct adverse health effects; lead to unwarranted patient anxiety and stress; and lower patient satisfaction and trust in the health system.
Here the study’s findings are relatively more optimistic. It found evidence on approaches that could eliminate up to half of waste in these categories. The current movement toward value-based payment, promoted by the Affordable Care Act, is intended to address these issues while removing their associated waste. The idea is to pay hospitals and doctors in ways that incentivize efficiency and good outcomes, rather than paying for every service regardless of need or results.
Putting this theory into practice has proved difficult. “Value-based payment hasn’t been as effective as people had hoped,” said Karen Joynt Maddox, a physician and co-director of the Center for Health Economics and Policy at Washington University in St. Louis and a co-author of another editorial of the JAMA study.
So far, only a few value-based payment approaches seem to produce savings, and not a lot. Some of the more promising approaches are those that give hospitals and doctors a single payment “as opposed to paying for individual services,” said Zirui Song, a physician and a health economist with Harvard Medical School.
At least on reducing drug prices, every leading Democratic candidate seems to have a plan
Lowering drug prices is a top priority for voters and an idea that President Trump has embraced as well, though he has yet to take major action. That has led Democratic candidates to come out with a variety of aggressive plans.
Bold plans to crack down on pharmaceutical companies has been a theme in the Democratic primary, with tough plans both from the more moderate side and from leading progressives.
Former Vice President Joe Biden, for example, also has a tough plan that would set up an independent review board to set a reasonable price for new drugs, among other steps.
Sen. Elizabeth Warren (D-Mass.) would allow the government to manufacture lower-cost generic drugs itself, while Sen. Bernie Sanders (I-Vt.) would tie drug prices to lower prices paid in other countries.
The "Medicare for All" plan backed by Warren and Sanders would also give the government much more power in setting lower prices for drugs.
Buttigieg would allow both Medicare and the new public option plan he would create to negotiate lower prices for prescription drugs, and those lower prices would be available to people with private insurance too.
So I think it's not really the plans or promises of cost reductions that they are lacking. Whether (and which of) their plans will be deemed credible is probably the real question.
As for limiting malpractice liability/lawsuits, 31 US states already do this, including big ones like California or Texas. It's not clear to me how much more can be gained in that area; it might be worth of a separate question, given the complexity of the matter. One of the studies cited by Wikipedia says
Overall annual medical liability system costs, including defensive medicine, are estimated to be $55.6 billion in 2008 dollars, or 2.4 percent of total health care spending.
This is clearly a big dollar number but also smaller than the other "waste" areas identified by the JAMA study, which doesn't even mention litigation.
Additionally, both Warren and Sanders seem to have a plan for reducing the costs of higher education (mainly by tuition elimination and college-loans debt relief measures, it seems), which may help with the supply of doctors as well, although the two of them don't seem to explicitly tie that with their healthcare reform ideas. (Biden has a more limited plan for tuition elimination only for two-year community colleges, and a very limited plan of debt relief, only for public service employees, it seems.)
If a proposal would fit the bill of just increased spending that seems to be Biden's plan, although hopefully I'm not mischaracterizing it by missing some big cost-reduction measure he proposes--he does propose one for medication, which I've covered in another quote further above.
The ACA guarantees that preventative health care services must be provided with no patient cost-sharing, but its authors were motivated in part by the view that outside of the preventative realm, Americans use too many health care services and should be encouraged to enroll in high-deductible plans that would offer insurance against catastrophic financial loss while discouraging the casual use of non-preventative medicine.
Biden proposes to make this whole scheme more generous across several dimensions, first by switching to the use of “gold” plans as the benchmark (meaning lower deductibles and copayments), second by making subsidies more generous across the board by reducing the share of family income that’s supposed to go to premiums, and third by eliminating the cap on financial assistance so even more comfortable families would get at least some help from the government.
Biden’s team estimates that making the ACA more generous in this way can be paid for through higher capital gains taxes on the rich. [...]
Biden “builds on” the ACA framework largely by relaxing the concerns about industry buy-in and patient overutilization.
So at least on this level of generality, Biden's plan is basically a less austere version of ACA. And it does come with a total price tag that does seems to be a net increase in the total budgetary cost to society, although mostly to be paid by the rich, per the above.
A senior Biden campaign official [...] estimated the cost of Biden’s plan to be $750 billion over 10 years.