Well, the counselor was on the bridge to assist the captain in first-contact situations, and dealing with alien diplomats. That, of course, is no reason for her to be there constantly. And, ya know, it was the 80s.
Children were on the ship because families were on the ship. The original concept was for a 10-year mission exploring deep space, far from home. Starfleet couldn't ask someone to be away from their family for 10 years, so the Galaxy class was designed to house whole families in comfort. Hence it's "hotel in space" look - it needed to be a pleasant place to live for 10 years. Of course, the writers threw the whole "10 year mission out of contact" concept away almost immediately.
Also, at the time (supposedly)* things were very rosy for the Federation. No Romulans, expansion everywhere, Klingons on their side. Life is great!!
*I always viewed the Cardassian War as border conflict, not particularly worthy of the Feds applying the full power of Starfleet.