Here is the objection I saw from the other thread. I don't agree with the objection, but I am trying to present it fairly:
Legendary actions are tied to PCs actions. You get a maximum you can use (we've seen three, presumably this number varies by creature), but you can only use them after a PC takes it's turn that round.
This is objectionable to some because the number of attacks the creature gets depends on the number of foes it is facing, and not it's own ability to make attacks. If it faces three foes, it gets three legendary actions per 6 second round, but if it faces two foes it only gets two legendary actions in that same 6 seconds, and against one foe it gets only one legendary action in that time.
So I guess the objection is this feels too metagame to some, and unnaturally controlled by the outside factor of "number of foes" which does not seem linked to the creature itself (there is nothing in the description of the creature that really explains why it would attack less against fewer foes in a given period of time).
To use a comic book analogy, the Hulk gets stronger the angrier he gets, and he gets angrier when he is hit harder by a foe - so his strength is based on the foe he is facing. Similarly, Legendary creatures attack more, the more they are attacked. So their number of attacks grows with the number of foes. But while Hulk's superpowers explain this growth in strength based on the foe's strength, there is nothing in the Legendary creature write-ups that explains the growth in number of attacks based on number of foes.