They're fine if they're short. I'd prefer elimination to longer games where a couple clear leaders after lucky first couple rounds are the only ones who can plausibly win, which I've also seen in a few enlightened modern games. Best case for those games is you spend the remaining 80-90% of the game playing spoiler or kingmaker, which is kinda shitty, or in the worst case the game's designed such that you can't do much about it, so you're going through the motions to see if you can manage 3rd place out of 5 (or whatever) for the rest of the game.
Monopoly's pretty short if you play by the rules and everyone knows how to play and isn't screwing around. I don't really like it, but I don't think elimination is the main problem. It's not like world-conquest risk where it typically drags on forever, well after the first player elimination.
[EDIT] economy-building games with low interaction between players and a significant randomness component seem especially prone to "well that player happened to go first and got the only good thing available to buy this round so has its benefit the rest of the game, and will proceed to stomp everyone else, obviously". There's a particular cards-based game with an age-of-sail trading vessel theme I've played several times that's my (least) favorite example of this: I've won, I've lost, both are fucking boring because you spend most of the game knowing where you're going to place and you can't even rage-harm other players out of boredom. Drawing a blank on the name. Anyway, I'd much rather be eliminated in a game like that.