IF you've tried playing a caster, then you will see that it IS a huge problem. You cannot use your best abilities because "legendary save". So you gotta cast your middle abilities to see if the monster will use them, all while the dm knows what will happen if all legendary saves get used up.
So you spend most of the time in a significant encounter unable to use your favorite/best abilities. It can also take more than 2-3 rounds, because the BBEG's will also have great saves, so they have a greater than 50% chance to resist any spell anyways and not need a legendary save. Dms won't waste the legendary saves on a magic missle or piddling damage spell, they'll save it for your best high level spells only. Which basically means you don't get to use them.
Imagine if a paladin had to wait 5 rounds before they could use a smite? Or a barbarian couldn't rage because the BBEG would just "turn it off", until you spent enough rounds burning abilities and eventually got lucky?
Casters leave these fights with a terrible taste in their mouths because its not fun. You spend the entire fight trying to do something, and consider yourself lucky if you did ANYTHING. Imagine playing your bard and 4 out of the 6 rounds you had no effect on the combat at all, cause the bbeg just said "nope!" or had good saves? BBEG fights are boring and frustrating for casters, and super fun for melee. Thats just terrible game design.