That's a point that needs to be answered by a virologist. But my guess is that what they would say to you has to do with reducing the opportunity to infect adults and opportunity for the virus to mutate. If it infects kids and their immune system fights it off, the virus's will mutate regardless, but the mutations that survive the kids immune system will be either those that were lucky, or those that were even luckier and are now resistant. New strains will survive to infect others and reproduce. In pretty sure that what a virologist would tell you is that our goal should be to reduce the incubators for the virus to the fewest possible. To that end vaccinating all the kids would be helpful. In the final analysis, the ideal, I am thinking, is to get virtually everyone on the planet vaccinated as rapidly as possible.
If you think in terms of a mammalian gestation period, for Homo sapiens it's 9 months. But a bacterium replicates in twenty minutes. I don't know what that time is for a virus, but it should be longer in accord with typical incubation period for viral disease. Bacteria double every twenty minutes in an ideal environment. twenty minutes later you have twice as many bacteria, all capable of mutating, then four times as many, etc. Replication time is going to be longer for a virus because they replicate intracellularly. I would think hours to a few days. But each infected cell will release anywhere from a few thousand to many thousands of virus. So in the course of a typical infection, even in a child, the opportunities to mutate will be many powers of ten. The viruses that infect humans need a human host. Kids may not be quite as hospitable hosts as adults, but they are still, nevertheless, going to be hosts.