You do make a good case that a caster probably won't be able to single-handedly take out a monster meant to solo the whole party. OTOH, if you have three casters in the party (and with half of all possible sub-classes being primary casters, that seems pretty likely), 3 uses of Legendary resistance just guarantees he gets through the first round.
A caster couldn't manage this anyway, but landing an occasional high level spell would be nice. Then again they'll fix this as more spells come out or I'll research some. Mainly a single target spell that blasts for good damage on a hit would help immensely. Unfortunately, those are concentration right now, I'm usually using my concentration slot for
fly while the cleric uses theirs for
bless.
In that sort of 'perfect storm' of all-proficient saves, high stats, MR, and Legendary Resistance, I suppose it might be. That'd have to happen a lot to outweigh everything a caster gets to do that other classes don't, though. For a game like 5e, that's balance. You virtually sit out some challenges, some of the time, so someone else can be center stage for a while. The problem might be that it doesn't happen to casters, enough, if you're only noticing it in these kinds of extreme scenarios.
I finished a module fighting a ton of dragons. It was quite common. That is with three casters in the group. We never once broke Legendary Resistance. Not a single time with a bard, cleric, and wizard in the group. Not once did we even come close to breaking Legendary Resistance for the following reasons:
1. Concentration slot needed for buffs like
fly,
protection from energy,
bless. Concentration slot for buff removes about a 1/3rd to a 1/4 of your offensive or effect spell options.
2. Martials had it killed at a fast enough pace it would have been a waste of time to try to break Legendary Resistance which would take well over the three or four rounds martials kill Legendary Creatures in. Action Surging fighters and Smiting paladins do a truck ton of irresistible damage. Legendary Creatures have nothing to slow down martial damage, especially if the martials have magic weapons.
3. Don't have time to use options that don't work due to the damage output of Legendary Creatures. You have to kill them fast or they kill you fast. No time to waste trying to break Legendary Resistance.
4. Limited high level spell resources. Your high level resources return only after a long rest. Spending even one high level 6th or above spell that has a high chance of failure means you expended a highly limited resource in a wasteful manner. Every good caster knows not to spend limited magical resources on wasteful abilities that have a very low chance of working.
I would say that if three highly experienced casters such as those in our group have not been able to break Legendary Resistance playing 16 levels, there is a problem with the mechanic unless that is considered working as intended. My friends and I are not neophytes, yet we did not break Legendary Resistance one time in 16 levels. We didn't even get close one time. I think we knocked off one or two uses in the entire 16 levels of play.
Even if you have to wonder how three highly experienced players playing the most powerful casters in the game that had a fairly easy time with the final encounter in
Tyranny of Dragons managed not to break through Legendary Resistance even a single time in 16 levels. I'd bet that our experience is not unique.