Making it a reaction essentially makes it an immunity for all intents and purposes, whereas the action it costs as written is, as mentioned above, redolent of the ability to focus and shake yourself free. In some respects that is almost more potent - the evil spell caster exults as the monk is bent to her terrible will...the laughter dies in her throat as she sees his eyes become unclouded. How did he shrug it off? Curses!
YMMV but it works fine as is for me.
I'd be more okay with that fluff if the crunch was actually congruent with it. The things that bug me are twofold:
(1) Usually, you make a saving throw vs. fear at the
end of your turn, not the beginning, so spending an action on Stillness of Mind has a nontrivial chance of being a purely wasted round. If your save vs. fear happened at the beginning of your turn it would be more attractive; a mulligan on fear, if you will.
(2) Many charm effects either outright disallow or at least strongly discourage spending your actions to end them. Let's say the spellcaster in your example had cast Hypnotic Pattern. In vanilla 5E, that means the monk is incapacitated, hence never gets a chance to break out of the hypnosis. Both mechanically and from a fluff perspective, that seems like the wrong outcome.
I've also considered making it a reaction but charging a ki point. Monks tend to have pretty busy reactions already (missile catch, slow fall, opportunity attacks, the 17th level Shadow Monk ability) so from a mechanical perspective that might be enough of a cost, but making Stillness of Mind ki-free does feel wrong from a flavor perspective. It
should be a ki-based ability, even if it doesn't have to be for class balance.
Note also that the Paladin of Devotion gives freedom from charm (and later, fear) to not only himself but all of his buddies. Allowing a quasi-immunity to fear/charm for monks (with or without a ki cost) does not seeem out of line to my design instincts.