>Let the children build up natural immunity
If a vaccine is safer, why? Framing a covid infection as "natural" is pretty twisted. It's not like primates have been developing immunity to this strain of bat poop for millennia. Pretending a natural infection is better because its natural is reckless. I bet, and I could be wrong, most people who had chicken pox wish they had the vaccine instead.
We do. You might want to read up on why the seasonal influenza is a seasonal influenza and how it is different from a new, pandemic strain. There is a reason children are ill all the time - their immune systems are naive with respect to (almost) all strains of influenza. That's also the reason the 1918 flu killed predominantly young people - it is conjectured that their immune systems hadn't seen the new strain yet, while older people had.
Doesn't sound much like the flu to me.
Even if "these young people" (makes me sound like a dinosaur, though in fact I'm in that cohort) don't care about that risk, they are wasting doctors' time, and taking resources away from overstrained health system.
So maybe I'd say: if you don't want to get vaccinated, without an overwhelming reason, then stay at home (so as not to risk infecting others) and if you do get sick, don't go to the hospital (as it was your risk you were taking).