I do have thoughts.
I don't think it has ever happened to me in practice, but as far as the rules go, it seems clear to me that yes, beasts are especially nasty as LMS's, because they get a clear turn, including the free Wild attack, and then they get to activate with full fatigue. Rampage!
I have personally been a bit sceptical about how destructive an LMS is, even when not a beast, so I have pondered some house rules for that (like here: viewtopic.php?f=3&t=42617
But it doesn't seem to me so far like an LMS is ever unfair or game-distorting - they might do a lot of damage, but the player that has multiple models left seems to still win most of the time. So getting the LMS benefits lets the losing player go down in a blaze of destruction, but they still go down, in my experience.
(This is just based on my own experience, not any analysis of any data.)
So if I want to tone down the LMS in my games, it's just to make that final "Finish him!" phase of the game feel a little bit more toned down, and less of a berserker frenzy.
Honestly I might even be tempted to cut out the issue entirely and say that the winner of the game is whoever brings their opponent down to their last card first - wiping them out totally is not necessary.
But either way... not letting Nero, Acerbus or any other beast with two stages left become LMS should be high priority for anyone.
(In my work, LMS means learning management system. Weird to write this post with that abbreviation.)