How is coming up with a rule based on our moral intuitions and then following that rule even when it means violating our intuitions any better than just following intuitions in the first place? How is it better to replace following intuitions with following an imperfect simplification derived from an intuition?

You can't get away from your intuitions.

We contemplate our moral intuitions and intuitively abstract rules from them, and have the intuition that such rules should be followed. Yet the rules may turn out to violate other intuitions. The problem is not rules against intuitions, but intuitions against intuitions.