I think losing control of
your character is not to be taken lightly in any context. Even within those contexts, it should be very clearly bound. Here's some relevant 13th Age 2E text for classic "mind control" conditions, as an example:
Charmed: You can’t attack. This condition ends if you are attacked by an enemy. You can use your actions to do anything other than attack or delay, since for the moment it feels to you like there’s some sort of terrible misunderstanding between friends. You know who your true allies are and can take actions to help them. But you also suspect that everyone else might be friends, though not to the point that you need to heal them or count them as allies.
Confused: You take no actions when it isn’t your turn. On your turn, you make a half-damage, no-trigger attack against a random nearby ally. If you don’t have a nearby ally, you don’t do anything on your turn. (See the Clarifying Three Conditions section below for the full explanation.) Important note, GMs: Confused shouldn’t be a “save-ends” condition when applied to player characters; it should always end at the end of the target’s turn or perhaps at the end of the turn of the monster that created the condition. (It can be a “save- ends” condition against monsters, but it rarely is.)
Charmed isn't even a risk of losing control per se, more just a constraint. Confused is, but it's very heavily constrained --- no burning good attacks, no dealing tons of damage, should only last a turn against PCs, and not deployed often (three times that I can see in the core book, more in older books, but the 2E rules explicitly recommend toning it down if you see it in a 1E book).
Point is, I agree, I think defined abilities with mechanical effects should be mostly completely agreeable, and they don't have to be "magic". At least one creature I ran into with a confuse attack produces hallucinogenic spores, that doesn't seem at all out of line to me. The more tightly defined those mechanics are, the better the chances of avoiding conflict or debate about overreach or railroading or whatever.
Also worth distinguishing, I think, is that losing control of
the situation is maybe a bit more open-ended but allowable, as long as it's open-ended in both directions, action and reaction. Diplomacy failed because of roleplaying and/or mechanics, the PC's vices are triggered because of roleplaying and/or mechanics, whatever. A system that accounts for those kinds of failures and encodes them in the rules of the game ought to present that as "the situation has changed: deal with it how you will", even if not everyone needs to use the mechanics all the time to lose control of the situation. It's this belief that draws out some of my ideas like "okay, you failed that, some later diplomacy is going to be at a penalty" (again, with mechanics or not).
EDIT: I forgot to point it out, but those two effects from 13A are clearly only relevant in combat. There are no specific "diplomacy x loss of control" or "vice x loss of control" or so on rules in it.