No 2 different targets trigger an AOO so you hit both of them with a powerful spell on separate turns.
Yeah that would be a powerful combo, but...it requires two different targets to trigger an AOO. It's not like that happens every round. Or every combat. Or every session. (Caveat: maybe it happens a lot more often at your table than at mine, and that's why you feel so strongly about this.). The forums are full of build ideas that depend on very specific scenarios; all of them sound OP until you realize those scenarios hardly ever occur.
Shield and AE are huge because with the right build shield can make a wizard extremely difficult to hit for an entire round. The only real negative to shield is the spell uses your reaction and some you tubers have suggested it should be banned. So it is already problematic and you are taking away the only cost of using it.
"some you tubers" have suggested a lot of things. I don't really consider that evidence of anything. So, no, it's not already problematic. (This is, in fact, the first time I've ever heard
shield described as problematic, except in the philosophical sense of how it's possible for you to react after you've already been hit.). Also, there's no rule saying the DM has to roll in the open or announce the attack roll, even though I know at a lot of tables it is done this way, so the wizard player knows if +5 will turn a hit into a miss. But if the roll is unknown it becomes easy to waste spell slots.)
In those situations in which you take elemental damage and you get attacked by a weapon, by different enemies on different rounds, this could be a nifty combo. Game-breaking? No. Not even remotely. Again, how often do these circumstances actually occur? (Is it game-breaking that a totem barbarian takes half damage from
all sources, every round, while he rages? No.)
(anecdotes deleted)
The most powerful reactions in the game are spells and in the hands of smart players this is going to unbalance the game more in favor wizards than it already is, there is no doubt about it.
Actually, there is doubt.
But even if you are right, a discussion about multiple reactions doesn't have to include wizards. It sort of feels...based on your examples...like you took the phrase "multiple reactions" to mean a base rule where everybody gets unlimited reactions on every turn, which I don't think is what anybody is proposing. There are lots of ways such a rule could be implemented, including making it a feature of a class or sub-class.