Toxe No. Classic fsm is objectively a poor choice for player state management. Beyond the simplest cases of player control, the pattern doesn't very well model all the finesse and complexity needed for something that plays and feels good. In a good action game, the player is almost never in a single discrete state. If you approach it like that you're guaranteed to end up with something that feels sluggish and unresponsive. You'll at least need to run several simultaneous fsms. This of course defeats the very purpose of using the fsm in the first place because you need to synch them which leaves you with the exact problem the fsm was supposed to solve.
It's fine for npc state management though, if npcs are sufficiently simple. But then again, a bunch of ifs would do the job just fine in that case.
But my main gripe is not with using the pattern itself, where adequate. You can conceptualize parts of your state management thinking in terms of discrete states just fine. I can't stand monolithic, bloated, turbo-oo implementations that are typically presented as "the solution"