My primary problem with fate points is a matter of how much it takes me out of the action to think about them in the context of a resource that has to be micromanaged.
The setting is Naruto, and Marked for Death beyond that. Chakra concerns are normal. Something that naturally happens as you get to be substantially more powerful than someone else is that you stop having to worry about running out of chakra when fighting them, because boosting stops being necessary. All good, right?
Well, when you throw fate points into the mix, things get a little bit more messy.
Ignoring Chakra boosting here, it'd change the numbers moderately but not too much. Say you've got Generic Jounin (60s for relevant combat stats) fighting Generic Chuunin (40s for relevant combat stats). The jounin has to use their fate points when fighting the chuunin here, because if they don't, the chuunin might get 3-4 aspect invocations off, putting them at 40+(5*3 or 4) for 55 or 60. That's got a pretty decent shot at inflicting a mild consequence, or filling out their stress at worst.
Okay, so the jounin takes out a chuunin, spending, let's say conservatively 2 fate points to the Chuunin's 3. Let's roll this, just to be fair.
Jounin: 60 + 7 (aspect) + 7 (aspect) - 6 (dice) = 68
Chuunin: 40 + 5 (aspect) + 5 (aspect) + 5 (aspect) + 6 (dice) = 51
Chuunin takes 6 shifts of damage and a moderate consequence. Next hit they go down. Now, the interesting thing here is... The jounin still has to spend additional fate points on the next roll (if reasonable/possible), because ninja are tricksy and it's entirely possible for the Chuunin to pull something out that would kill them (or at least inconvenience their mission, like an explosive tag). Still, let's ignore that.
Jounin is at a net -1 Fate Points from this exchange. I was very generous with not rerolling their low roll there -- in the context of someone actually in a life or death situation with an unknown element, I don't think it'd be unreasonable to expect them to spend one. Still... If the jounin was lesser-skilled, a 50-dice combatant or something like that, they might well have had to spend multiple more fate points in the engagement.
After the fight, they're down one fate point (they won the conflict, getting them a fate point back). Not a problem under most circumstances (particularly outside the Chuunin exams, which is, honestly, why this is relevant at all), but if it turns out instead that the Jounin has to fight multiple chuunin, things turn out very differently. Given a normal-ish amount of them (7), they could well run out of them or run out of aspects to spend them on.
What happens then? Maybe nothing. Maybe the jounin slugs it out, but maybe they lose out to the chuunin due solely to the fate point economy. I'm not sure how reasonable this is.