I went to shul regularly starting at six. Did I understand everything going on around me? No, but I could see how important it was to my Zayde, and I did take an interest in what was going on, and being discussed. I didn’t run around, yell, or throw temper tantrums because I knew that this would not be tolerated. I was taught the shul was not just someone’s living room but a sanctuary of special holiness. Before passing from the men’s cloakroom to the shul itself, I would say the “How goodly are your tents, O Yisrael…” that generations of Jews have said upon entering a shul.
I do have sympathy for people who have really bad memories of going to shul as kids, and want something better for their children. Many shuls have a children’s service in the basement or social hall of the shul. These seem to be fairly abbreviated, and kids aren’t there from the beginning to the end of davening. I also don’t know whether kids find this to be more than a temporary diversion or if there is a long lasting value.
I am bugged by parents allowing kids, sometimes as old as ten, to start eating the Kiddush before the adults have even had time to wash for bread. Some of the parents will be eating with their kids, not having washed for bread themselves. This is really bad Chinuch.