On topic: I could see myself playing Dominion for money, but not for any big amounts. It's my hobby, not my job.
Off topic: I want to object to a few points you're implying.
lately i've been thinking about how widely accepted variance is in eurogames, even at the most competitive levels, compared to the utter hatred for any of it it in competitive video games. i'm sure a number of you are familiar with smash bros. tournaments banning items since they're highly random, and top players in any game get highly frustrated if a 2-out-of-3 set doesn't determine the better player.
One of the main complaints about EVO this year was that it wasn't best of 5 until near the very end. Now, EVO couldn't do that because of time constraints, but it feels like you're implying the winner of every fighting game match is the better player. Which is completely absurd - upsets happen. When you're guessing how the other player is going to act, you're going to get randomness, even if the game doesn't have any randomness in it. What matters for competition is whether the player feels like they have a big enough impact on the outcome of the game.
It's possible you're talking to the wrong people about this. If you ask eurogame enthusiasts, of course they're probably going to say that variance is part of the game, because anyone who doesn't like that part of eurogames isn't going to hang around eurogame communities.
I'm also confused what grounds you're using to generalize this to outside just Dominion.
i wonder if a major reason for this difference is the fact that IIRC there's no big competitive eurogame with serious money on the line. i doubt i need to tell you about the prize pools for MOBAs and the like, and that adds an extra "gut punch" angle to losses that are out of your control.
If there was money on the line, I'm sure people would care more, but they'd also heavily object to tournaments that don't give enough games to determine the better player with high certainty. See: Smash at EVO. People just straight up lose games of Magic: the Gathering to drawing too many or too few lands, and there's thousands on the line there.
it seems like in this world, luck elements are the only way designers have managed to prevent games from getting old after extensive play. i suspect the obvious swinginess would limit people's desire to put up money for tournaments or even a first-to-10 against one opponent (a common type of "exhibition" in fighting games). as my entire reason for learning these games is competition, it makes me wonder just how far even a game as great as Dominion can go in that regard...
Luck has never stopped sufficiently devoted players from placing money on the line. There are the obvious examples like poker, but there are also smaller things. Mario Party money matches have happened. I know because I watched a livestream of one, and it was hilarious. There will always be people looking to put their money where their mouth is.
As to designers relying on luck elements to get replayability: can you think of any alternatives? I can't. In eurogames, players have to implement all the rules themselves (meaning they have to be simple). You also can't rely on forcing more mechanical skill, on players pushing each other to get better at hitting frame-perfect timings, because eurogames are almost always turn-based. Adding randomized setup is a simple way to get replayability without changing the complexity of the base rules - it's no wonder that so many games do it.
From your post, I get the feeling you believe that
1. More people will play competitively if there's money on the line.
2. Luck makes people more hesistant to put money on the line.
3. Therefore, luck is bad for the development of a competitive scene.
To which I'd say,
1. More people play competitively if the game is fun. The vast majority of players will never be net positive in money after a tournament. They're there to challenge themselves and become better players.
2. I've never heard people say they didn't want to enter a tournament because the game was too luck based. They don't enter because the game isn't fun anymore. And yes, sometimes that's because they lost from bad luck.
3. So, I don't think luck stops competition at all, as long as it's reasonably small, and I'd say it is reasonably small in Dominion.
There are many more important factors for growth in a scene. Barrier to entry, easy to follow for spectators, whether there are storylines for famous players, and so on. Dominion is held back primarily by the first two.