Now maybe this isn't universal, but from what I've seen, players don't like Legendary Actions very much. As you learn to play the game, you get used to certain limitations. I can move so far on my turn. I have to make do with one action, one bonus action, one reaction. You plan your turns based on this, heck you build your character over time with this in mind- someone who likes dual wielding isn't going to load up on a bunch of bonus action abilities, as an example.
Then you're fighting some monster and out of nowhere, it's now doing all this extra stuff when it's not even it's turn. And you have no real way to react to it or plan around it, it just does it's thing when it wants to. And even if you did ready an action to deal with it's Legendary Action, that makes you less effective on your actual turn....and it doesn't need to weaken it's effectiveness in any way to get this effect.
I've heard terms like "boss magic" or "NPC powers" or "total bs" thrown around by people frustrated by this. Now, just imagine, you run your company based on, oh, I don't know, call it 70% customer satisfaction (disclaimer, all numbers are made up and imaginary, this is a hypothetical scenario). You have frequent polls to see what the customers have to say. Now let's also assume that only 25% or less of the customers are DM's who want to run challenging boss encounters. That's a potential 75% of people who can be frequently annoyed by Legendary Actions (and their cousins, Lair Actions). And you only need 31% of your customers, less than half of all consumers, to voice their discontent before you tell your developers "find another way".