Unless you are a terrible healer the only necessary fights to control your fairy are in coils 5-9
If you are using some crazy moogle ex strat where everyone is grouped up, then maybe there as well for the aoe heal
And if you don't lag it probably helps with titan ex if you're with a horrible party that dies a lot

Other than that, there are no situations in the game where you should ever need to control your fairy. And anyone saying there is, either parties with people in i55 gear, or parties with people who don't know how to play their job.
Every dungeon is a joke and can be healed by a sch even without a fairy (e.g. I can skip summoning my fairy, still keep a semi-bad party alive, while doing damage on the side)

every ex fight (except moogle) is pretty straight forward and easy. And fairys aren't hugely important (although again they would help if you party with bad people. Like if dds can't avoid aoes in ifrit ex the aoe would be useful)


To be honest in most dungeons eos can handle healing the entire thing, while you cleric stance and dd the whole time.