It's a matter of our fairly strict drug regulation. You can't approve a drug for a population it wasn't tested on. Tests involving kids are always harder and more expensive and Covid harm skews strongly older, they didn't include kids in the original test population. After success Pfizer started doing tests on kids, the 12-15 band has already been approved and they're working on 5-11. Presumably there will be another round of testing for the under 5s.
I see. Then I'd say that lack of flexibility does not seem to be a good idea. I mean, the fact is that children aren't getting the vaccines, and then they're getting infected, and then they're passing the virus to the adults in their families, and some (many) of them are dying or suffering serious long-term consequences, which is very bad for them of course, but also of course much worse for the kids than the expected negative consequences from the minimum risks of a vaccine - assuming the risks aren't much greater than with a "dead-virus" vaccine (granted, Sinopharm's vaccine was tested also on children in China, but a lack of speedy tests is also a problem. )
Meanwhile, over here, in spite of a seriously incompetent government, a much weaker health care system than America's, mediocre laws and worse enforcement, kids older than 3 are getting vaccinated, which predictably will have better overall results for them and for the rest of the population than the US approach. I think the US should upgrade its approach on this one.