First off you threw in a ringer--nicer house--like the old Reaganites ranted about the Welfare Queen as though they were in abundance, a cheap trick
I'm fascinated to know why it is that someone with a higher amount of income isn't on average likely to be living in a nicer house than someone on a lower amount of income. That is, if you have 2 identical people, earning the exact same amount, and one has health insurance and one doesn't, then the person who doesn't has more money to spend (initially, before the hypothetical medical emergancy rears it's head). Thus it seems logical to say that on average that person is going to be able to afford to live in a nicer/better/more expensive house. I fail to see how pointing this out is a "cheap trick". The house could still be in a slum, since I'm talking about the relative 'niceness' of the two houses, not the absolute values.
Ultimately it's about risk and reward though, as I mentioned before - if you don't take insurance you get to benefit from the full upside of your risk (i.e. if you don't take insurance and don't get any medical bills, you keep the full 'profit' - the amount of money you would've been paying on the insurance). If you're proposing limiting the downside (capping the payment), then you'd need to restrict the upside (or else it's unfairly penalising those who do take out insurance relative to those who don't, in effect), which basically means you end up with a compulsory health insurance system - either take out private health insurance, or take up the state-provided one.