That's because I think long-term, single-payer is the only sensible way to handle health care. We have (the US has) a truly screwed up healthcare system that (nearly) everyone acknowledges is inefficient, too expensive, wasteful and less effective than it could be. Looking at other countries, this is obvious.
Given the money involved, getting to single-payer will be a long-term project; now even longer, to clean up the mess currently being made. It'll involve more fighting, take longer, and be a more expensive transition than anyone likes.
Given all that, we have to start somewhere. I'm happy to start in my state, even though I have great (employer-provided) healthcare, and could easily pay for my own if I didn't.
There's also the aspect of doing the right thing, even at personal cost. I think single-payer is the right thing to do.
So that's why.
I think such a system would work much better for the US as it's easier for the state to build such a framework than to come up with health care for everyone. The NHS (UKs single payer health provider) is the biggest employer in the state, which gives you some indication on how complex it is to provide universal healthcare for everyone.
If you only care about yourself, ask what would happen if you developed a serious illness or were in a bad accident: very few people have the millions of dollars needed to survive something like that and you have no way to know if that's going to happen or avoid it even if you did.
I'd say I'd gladly pay more in taxes not to have to worry about that except that the experience of every other developed nation suggests it'd be a massive price reduction.
Practically speaking, worrying about health care (and the lack thereof) is the number one reason that makes it hard to start your own company...unless you are already wealthy.
For one, having health care tied to a job is a big burden. As an employee, it makes choosing to leave my job extremely worrisome, especially if the federal government repeals the pre-existing conditions portion of the ACA. I can never leave my job while I am sick, or my kids are sick.
Tying your health care to work also makes it harder to start a small business. You need to offer your employees health care to compete for good workers, but it costs a lot more per employee for a small company to get insurance than for a big company (a big company can get a better deal because they have a larger cohort).
An even more insidious fact of employer based health care is that it doesn't cost the same for everyone. If I am going to hire someone and offer health care, it will be MUCH more expensive for an employer if the person is going to have their children and/or spouse covered as well. It will cost more if they are older. It will cost more if they have medical conditions.
This adds a perverse incentive to employers to favor hiring younger, single, people. As an employer, I should not be worried about the marital and familial status of my employee. I should pay them the salary we agree to. There are laws against discriminating against some of these groups, but if you are a small company it makes a huge difference to your bottom line.
I also fear getting a major illness. Suppose I am doing everything right, working and I have health insurance. I get cancer, and it is treatable, but it might take years to beat. I start out fine, with my good insurance. One year in, it becomes clear I can't keep working my job, so I am let go. I can keep paying for my own insurance through COBRA, but my savings are dwindling because I am no longer working. Even if I am suddenly able to work again, I wouldn't be able to get new insurance because of my pre-existing condition.
There is literally NO amount of planning I could have done to avoid this situation. I was doing everything right, and an illness can make you go bankrupt.
The last argument for why I would pay more for health insurance is a moral one. I find it immoral to not provide basic health care to everyone. I feel it is an obligation we have to each other, and the most efficient way to meet that obligation is through a single payer system. Insurance works best with the largest possible pool of people to spread the risk, and you can't get a larger pool than everyone.
So yes, I am willing to pay a little more for a single payer system, for both selfish and altruistic reasons.
The question is, why wouldn't a society or community want universal healthcare for it's people?