One of the issues with that argument is: If Biden's workplace vaccine mandate goes through, many of the remaining people who decide not to get vaccinated simply won't have insurance, given they'll also be out of a job.
Instead of paying more into the system, they'll be paying less. They'll still end up in the hospital. Defaulting on the hospital bill doesn't seem unlikely for many in this situation.
This is the biggest reason why this move by Biden is an idiotic gambit, relying on the hope that most of the holdouts are simply on the fence and need a manipulative push. He may be right, but the cost of being wrong could quite literally be large swaths of the US Healthcare System.
What's more, we're seeing concerning numbers of healthcare workers leave the industry. ICUs are not, generally, overfilled because they're out of physical beds; they're overfilled because they're out of people. No one in power is talking about this. Hospitals lose nurses making $70k, then turn around and pay $8000/week for travel nurses. Those nurses that left? You guessed it: many are trying out travel nursing. The rest are burnt-out.
The crisis really is not in the unvaccinated; its in our healthcare system, and it was growing long before the pandemic. A fractionally small part of me actually believes what some in the really, really fringe-right are saying right now: the administration wants the healthcare system to fail, because its another crisis which can be pivoted into single-payer or even nationalized healthcare. Well, its their fear, but its conversely my hope, because at least that would mean the people in charge have a medium term strategy for what seems to be inevitable at this point.