Sure, as long as they all equally have robust immunity and do not interact with anyone outside their group. Bring in one kid with a weaker immune system and guess where the virus is going to evolve.
Except that didn't happen. I moved DD to a private school in '20 in the next county over because it was open while both public and private in LA County were closed through the school year in '21. There were no big outbreaks, Grandma did not die.
We did it your way, so this is pure conjecture, but what would have happened if we had NOT shut the schools down and, those who were not getting seriously ill (the kids), all got sick first and the disease mutated before it got to be wide-spread? Would that not have saved lives?
Before you answer, that's kinda what happened with my family. My kids' HS had what we called the "plague" in December '19 -everyone was sick. The sickest any of us got was Christmas of that year. Urgent care after urgent care had no idea why DW in particular was so sick. After that, yeah, we got it once or twice, but not seriously enough to even get tested. Loss sense of smell was the only way I knew I had it. DD was tested because she got Strep Throat. I got sick after spending Thanksgiving with my (fully vaxed at the time) 80 year old uncle in '21. It was fine, would do it again.
If you want to get the shots, knock yourself out. If it's not worth a Dr's visit, maybe re-think that. It's up to you, but I'm 100% out, pandemic over, time to learn from our mistakes.