If this were the case, we wouldn't be seeing such a sharp increase in vaccinations after the arrival of Delta.
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Here's another reason your "people want to be free and catch covid" argument lacks merit - Palm Beach County Schools, the 5th largest school district in the state, recently changed their mask policy from voluntary opt-out for all students with a signed form to medical opt-outs only.
When parents were able to opt out, you know how many did? Six percent. So 94% sent their kids to school with masks on. Finally, with high community transmission and after having sent 1,400 kids home to quarantine, the school board realized they were risking the health of too many children and families just to keep 6% of parents happy.
So no, people would not rather be free and catch covid. No one is arguing for a complete lockdown, but if we had statewide, common sense mitigation policies, we wouldn't be in the position we're in now. New York's population is just below ours and they don't have even half the problems we're having.