This is pure anecdata on a data thread, but I've written before about being conflicted about any potential covid vaccine for my young children.
I wouldn't personally mind them having it, but they wouldn't want it due to the needle. So I would be forcing them into something that they don't want, that wouldn't really be for their benefit.
They've been exposed to covid before, to symptomatic people and they either caught it and were asymptomatic, or they didn't catch it. Now, they could, I accept, encounter it from one of their school buddies and maybe catch it? But when their school chums' parents have been vaccinated that then already lowers the risk of children being exposed? This is just my musing.
I've also talked before on here about the covid outbreak among my DH's side of the family due to our errant rule breaking, which I partook in at the time and miraculously escaped catching covid.
In that outbreak, no children under 12 caught it, despite being in households with people with covid and absolutely no distancing. Maybe they did have it, but they certainly weren't ill/displaying any symptoms (obviously we were all isolating at the time).
So I remain very conflicted about any potential covid jabs to children.