This is a bit long, but we can't answer the question without getting the full context in front of us.
First, let's start by asking what people did before there was insurance:
(1) They didn't get sick or have accidents.
(2) When they got sick or had accidents, they just died immediately and saved society the burden of caring for them.
(3) If they didn't have enough resources (including, but not limited to, savings) people who were close to them -- people in church, sodalities and fraternities, etc., friends, neighbors, relatives, sometimes even strangers would help them until they got back on their feet. And life went on.
Correct answer? Drumroll, please ...
(E) All of the above.
If you don't understand that much, we can't talk meaningfully about this.
Second, let's ask what happened with insurance:
(1) Check. Lots of people were still not needing help. One point of difference, some of these people are voluntarily joining the strangers I mentioned above who help other people in need, by contributing to one of many independent companies that establish these pools that we talk about.
(2) Check. Lots of people were still getting sick or having accidents and dying. One point of difference is that some of those who died were covered by insurance and some weren't.
(3) Check. But with more insurance available, fewer neighbors and strangers feel the need to get involved, unless they get involved by buying insurance. And, with money going out in insurance premiums, there was less available for savings.
There was a new way of making a living called working for (or running) an insurance company. (I'm speaking loosely here, some of those weren't really companies in the legal sense. There were several legal categories besides company for insurers. I think some of those categories still exist.) This is not a strictly bad result -- has both pluses and minuses.
Also, it became easier for people without good neighbors, church or other abstract community, close relatives, etc. to get help. This contributes to alienation, but it also contributes to reintegration. Again, there are both pluses and minuses.
Unnoticed tertiary results?
Insurance companies start making rules that our government is Constitutionally forbidden from making. This is an essential bit of information here.
Third, let's ask what will happen with mandatory insurance.
(1) Will people stay healthy?
We should hope so. We aren't sure, however.
(2) Will people get seriously ill or have accidents and die?
How can we expect it to be otherwise?
(3) Will family, neighbors, friends, relatives, people in their abstract communities, and strangers still help?
Ouch. Yes, but everyone is paying insurance, so it's harder for those who are not making a lot of money to help. And most people don't make a lot of money.
Wait, let's back up to (2). Insurance companies are motivated to reduce risks, so they will be making even more rules to try for force people to be healthy and safe.
They will also escalate the social narrative about "responsible behavior" as if conformance to any arbitrary set of rules could really be called such.
Does letting the insurance companies get their fingers in every little aspect of individual lives actually make anyone healthier, safer, or more responsible?
I hate to be rude, but use your common sense --
When was the last time society was benefited by someone, or by some group, asserting they should be allowed to play God?
You say the rules aren't that bad, but I'll point to some examples. Flu shots are considered a moral requirement in Japan, in no small part due to the social narrative from the insurance companies.
Do they work? For some people, they seem to work, but there is a growing percentage of people who have bad reactions and end up becoming seriously ill, permanently disabled, or dying. The insurance companies started backpeddling on this recently.
Surely things are not that bad in the US?
Oh! Think of the CHILDREN!
I am thinking of the children. Most vaccinations were recommended not to be given before six months or so for very important biological and medical reasons. It was not that they were not recommended before six months, they were recommended against.
But the pharmaceuticals salescrew works on the insurance salescrew and the staffs at hospitals, and "Oh! Let's just get them done with and over before the parents forget!"
And the vaccinations don't work like they used to. They change children's biology, and the new generation is, no, not superhuman by some chemist's accident. The new generation is susceptible to a new class of diseases that are harder to deal with.
Vaccinations are not the only problems here.
And, finally we get to the question of mandatory premiums.
I've been sidelined from my original career path for more than fourteen years or so. I've been working entry-level/temporary jobs, just barely making a living. I haven't been making enough to send my kids to school, and that fact makes me something of a social pariah in Japan.
I just crossed an age line three years ago where it has become difficult both to renew the contract, and to get a different entry-level/temporary job. I paid about $150 yesterday for August's mandatory insurance premium when I don't have money for August's rent or next week's food.
Fortunately, because I live in Japan and not the US, I don't have to pay an additional mandatory premium to the fatherland. (Fortunately, somebody who wrote the law realized we expatriates would have good cause for class-action suit against the government if they tried to double-down on us.)
(JFTR, I'm writing this while I wait for a friend to give me permission to use her as a reference on a job application.)
There are a lot of people in any country who are physically healthy, who, for reasons they really don't control, are one step away from being in the sort of situation I am in.
Now do you understand why the question of mandatory insurance, and the ACA that underlies it, is considered "nuanced".