Technically, our taxes are used for all kinds of stuff we don't directly benefit from and you can argue that the insurance premiums we pay are paying for someone else's treatment.

I think another argument is that it'll be less effective (ex: longer wait times, etc) and that people will abuse it, ex: in Canada, I used to see people show up to ER because they were sneezing and I've seen people wait forever to get a doctor, etc, you're much less likely to do that if it costs you something.