I'd disagree that it's about making insurers be more efficient.
Basically, the idea behind that rule is that the MSF should be the administrative costs of running health insurance, plus any profit-taking by the insurance company. By capping what percentage of premiums the company can collect for their own expenses and profit, that cap more closely links premiums to health care costs.
In the past, if investors wanted to see a 20% annual increase in corporate profits every year, instead of being the most innovative, best-run businesses, insurance companies could just gouge their premium holders, say "costs are going up," increase rates by 30% to 40%, and pocket most of the increase.
Another variation of this scenario, or even a multiplicative effect, is if the corporation tries to boost their profit margins by investing in riskier, higher-return investments in the stock market. If the stocks go bust that year, they mask the consequences of their own failed investment decisions by just boosting premiums. If they lose money and still want to see a big profit increase, then the premium payers get double-screwed.
By making a minimum percentage of premiums collected to directly to payment of medical claims, it prevents companies from padding profits or making up for investment losses via increases unrelated to actual health care cost changes.
If they remove that requirement, companies will add premium charges because they can. This is the problem with for-profit health insurance. If you have a mandate to maximize profits, you need to maximize premiums collected while minimizing premiums paid, which does not fit for a product like health care financing and the health care system in general.
Medicare and Medicaid generally run at about 2% to 4% administrative cost. Of course, they don't have to have any kind of a sales or marketing presence, but I've seen non-profits that must compete in the general marketplace that run at about 8% to 10%, so the difference in allowing more than 15%/20% and not is almost entirely the amount of profit they take or how lavishly their C-level executives want to compensate themselves.