It's largely for this reason exactly that the Church requires celibacy of her priests. The Church knew, long ago, that if a man is married, he is going to put most of his efforts into his marriage and family, as he should. Being a priest in a Catholic parish requires one's full attention to be on the Parish, and its members, so not being married means he doesn't have those family needs vying for his attention and efforts.
Yes, there are denominations that have done fine with a married priesthood, but the Church has been served well for centuries with celibate priests, and the Lord will provide workers for the harvest, if we keep our trust and our eyes on Him.
Again, both illegitimacy and the current problems would be alleviated by allowing priests to marry IMO, thus drawing a lot of quality men into the priesthood. As you noted, priests in other demoninations do just fine at balancing work and family. In fact, this can allow a priest to have even MORE insight into what afflicts suffering people whom they must counsel. Marriage is not a lesser state.
You missed my point on this one.