Millions of people will just (continue to) take the risk, get sick, go to hospital, and die (in decreasing proportions), incurring substantial personal and social costs along the way.
Accepting only vaccination as evidence of protection reduces the size of that risk-taking population, and the concomitant social costs.
Should there be a third policy option - accepting test-verified infection and recovery as of _now_ as evidence of protection, but discounting future recoveries? Based on the observational studies cited all over this thread , probably yes. Seems like associated costs would be higher though, and the only benefit would be less gnashing of teeth here and elsewhere, so its understandable the CDC isn't rushing to implement it.
Should those people just be allowed to assume the risk? Not while the costs are predominantly social. Insurance (or tax-payers) pay the financial costs, healthcare workers bear the burden of treating a preventable illness, and we all assume the risk that healthcare resources will be stretched to the point of unavailability. While risk-takers do pay into the same system, their premiums don't yet reflect the increased expected costs of their personal choice. While ICUs often run close to or at capacity in one hospital, rarely do they run close at every hospital in a region, as is happening in the south and will happen elsewhere. While it would be nice if there were more doctors, nurses and facilities able to treat patients, we're at war with the army we've got.