I don't really see a problem. Even non-intelligent creatures will have some kind of behavioral pattern in combat, to taunt them you just need to exploit that to make yourself seem like the primary target. To taunt an ooze you may try to make yourself look just the right size for the ooze to consume, while to taunt a construct you could say something that triggers the targeting algorithm in a certain way.
One of the slippery bits here is that when you put the
effect before the
cause, you lose a lot of people's investment. If I have a character who can taunt, I don't expect it to double as construct hacking or natural knowledge. I expect it to annoy intelligent NPC's - that's a "taunt." I'd kind of expect your Charisma to feature into it. I'd expect to be able to affect foppish nobles more than it'd affect a town guard. It wouldn't necessarily cause folks to attack me (that'd depend on the folks, really).
This is part of what works against a "mundane" character (especially outside of combat) - if I can taunt, that's a verb, not an outcome. It's a cause. The effect it has may be somewhat defined, but no more so than a longsword. A longsword deals 1d8 damage, but it also cuts ropes, slices meat, gets you noticed as an armed brigand at the bar, is an heirloom from your grandfather, etc., etc. It's a prop that exists in a world, not just a button to push that deals 1d8 damage. A taunt is a thing you can do, not just a button to push to get creatures to target you.
Once we start justifying the effect by changing around the cause, we're playing a bit backwards for a lot of people. The point of having a taunt is not so that I can control targeting in combat - it's so I can roleplay a SUPER ANNOYING character who can get under peoples' skin.
Magic doesn't have to deal with this kind of thing because arbitrary limits and abilities are fine if "it's magic." If I use my psychic powers to force an enemy to fight me, I don't care too much if it's an ooze or a construct or an undead or a town guard or foppish noble or what. Magic knows what a "creature" is, magic can make a "creature" fight me, game on!
If you introduce a mundane taunt for the purposes of controlling attacks, then you're in some misty territory where it doesn't always work like a taunt (yes, you can...annoy...the...ooze?) or it doesn't always work for the purposes of controlling attacks (you make the foppish noble angry and he storms off in a huff).
It's like the difference between a mundane "insult" ability and
vicious mockery. If these two things work like each other, but are distinct, you get a buttload of corner cases, questions, and kinked assumptions. Just give a fighter
vicious mockery and dodge the whole circus.