At one point in time, Riot took the stance on mana burn as 'anti-fun,' because it removes the player effected by it resource pool and as such, removes their ability to act accordingly. I'm not sure if their stance has changed recently, but I hope it doesnt.
If mana burn was reintroduced (because it was on Wit's End at some point), you'll have a problem where champions that need mana to use abilities now also have to account how much mana could potentially be removed which could force some champions out of play in any match up with that mechanic in it. If the mana burn mechanic was too weak, it'd be virtually useless. Too strong? Well, mana reliant champions may as well take a back seat. Mana burn is just right? You still present a situation where once your mana is below a certain threshold, you may as well be silenced. This doesn't even take into account how, or if, it'd effect rage, energy, or whatever a random champion uses on it's.
TLDR: I feel the mechanic would just feel horrible or nonexistent.