Settlers of Catan has a few "dead man walking" situations, but they're somewhat rare.... Especially because the optimal strategy in Catan is to trade with players weaker than you. So all "dead men walking" get boosted by the stronger players. The 1st place player never wants to trade with the 2nd place player, or vice versa.
"Ticket to Ride" has more dead-man walking situations, where you know you've messed up but nothing can be done until the game is over. And because the game is elimination free, you feel like a jerk to leave before the game is over.
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The goal is to find a game that strikes the balance. Keep everyone playing, but make everyone feel like their contributions (even if they're behind) are noteworthy.
Carcassonne is probably the best.
The optimal strategy is to trade with players weaker than you who have something worth trading.
I've had many games where the "dead man walking" comes into effect because a player generates too few resources or not in demand resources (usually by bad initial placement) and therefore is only useful to squeeze for the occasional resource. They can't engage in constant trades because they literally have nothing, potentially not even as a space blocker. So optimal strategy becomes mostly ignore them except for kingmaker.
The situation where you have a clear "dead man walking", even when you did everything correctly, is when opposing players block you in with roads, preventing your expansion.
Once one of your initial 2 villages are blocked, the 2nd village becomes a target for blockage, because everyone knows that blocking your 2nd village will effectively eliminate you from the game.
Not "really eliminate", you're still a player and are kinda forced to play. But you can't make a 3rd village, and basically have no pathway to victory. A few unlucky rolls, or an opponent's lucky "Road Building" card, can bring up the road-block strategy extremely quickly.
A lot of people also play with the houserule no trading because there is too much kingmaking in trading. It's too easy to place aggressively for ore if you know you can trade for whatever you're missing of the settlement. If you have to 4:1 it's a bit more of a tradeoff.
Otherwise you're all sitting around a board that randomly generates resources for you to spend and sorta get in each other's way with road and settlement placements. If you want semi-solo Euro games, play something with way less dice variance!
The trades and dynamic that arises from the mechanic are pretty much the only reason to play imo. Otherwise the dice mechanics are way too strong as you point out.
But as you can see, the idea quickly became way too complicated and we never implemented it.
Removing trading sounds like a terrible idea. Being able to monopolise a resource just to trade it for what you really need, is a feature, not a bug. Some resources are rare, and you need to take that into account during placement.
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.