Mod-80, if all your child is doing at shul is playing, then yes that may be problematic.
However, I think shul is more than JUST about davening. Its about community building. Obviously not during services 🙂 But my son can’t sit through all of davening.
Being part of a Jewish community is extremely important – its often the glue that binds people to Judaism when times get tough. People are there for support, love, help and anything else.
That’s why my shul has a kiddush every week (usually small unless there is a simcha). It brings everyone together to build relationships within the community.
But if all your kids do is play and never see the inside of the sanctuary, that is a problem.