"children that don't get the vaccine are going to be exposed to the spike protein via covid itself, and that's going to be worse than an exposure via the vaccine"

Only for adults. Children get the virus, but don´t become sick, so risk is still small compared to the vaccine risk.

"if enough people get vaccinated, we can effectively stamp out covid and stop the mutations"

You mean like we stamped out influenza? Maybe in theory, but in reality the virus always escapes the vaccines. He is always one step ahead. It is just a myth, in order to make the vaccine companies rich.