For me, cheaper premiums are not even the selling points of universal healthcare. It's selfish hedonism:
It's emergencies - No tax will exceed 100% of my annual salary, so why should a surprise medical bill I couldn't possibly avoid (T-boned when I had the right-of-way and thought I looked for cross traffic?) bankrupt me?
It's uncertainty - Sure I'm middle-class now, but what if software really is in a bubble, and I'm broke in 15 years? Voting for my own interests has to include voting for things that _could_ plausibly happen in my future, not just what's happening to me this week.
And it's the social graph of private charity. If my friend is a little worse-off than me, should I be guilted into donating money to their medical costs? I'm nowhere near the philanthropist class. Why should it fall on me? Not having a safety net punishes middle-class people who care about their not-middle-class friends and family.
Paying with taxes is much fairer - No surprises, no desperate clinging to my job, and no guilt.