Can you give specific examples of FATEs where you feel this is an issue?

The only FATE I can think of where the normal mobs in the area are even mildly annoying is The Eyes Have It in Coerthas Central Highlands. Even then they're only a problem if people ignore them while focusing on the boss and the boss adds so they swarm the healers. If I'm organizing a group for that FATE, I make sure there's someone to tank the boss then I keep rounding up everything else so it can get AoE'd.

If people just kill them instead of trying to pretend they don't exist, there's no problem. It's also extra XP since most people use jobs they're leveling when doing FATEs.