If you want to play the equivalent of "no items, Fox only, Final Destination" in Dominion—and I'm not saying you do, but if you did—I think the closest analogue you could get is to find the set of 10 Kingdom cards that most rewards skill, and only ever play that board. Just play the crap out of it. That way you never have to experience the endless variety that makes Dominion so much fun. It's not a perfect analogy, of course, but you can't get a perfect analogy between a fighting game and a turn-based card game.
Incidentally, when I introduced my partner to Super Smash Brothers, we had the problem where I was significantly better than him. And I thought, based on stereotypes, that we could make it more luck-based by turning up items. It turns out that items tipped the scales even more in my favor, because I actually knew what all the items did, and he didn't. This is an excellent illustration of how luck and skill are orthogonal characteristics of a game.
I agree with your conclusion but your reasoning seems rather flawed. The additional advantage didn't come from him being accustomed to the random way the items were distributed, but from knowing the mechanics of the items themselves, which isn't inherently random (except for a small subset of them, like pokeballs)
In Brawl, a side effect of using the "Contra Code" to play Zero Suit Samus put her suit parts onto the floor, which could be thrown like a pitcher's fastball and dealt lots of damage. It was incredibly easy for defending player to pick up some of them to use for themselves, you just tap A when the part is thrown towards you and you catch it. There were infinite examples of players with a few dozen games against ZSS trying to deal damage with the suit parts as well as 3,000 game veterans of ZSS did, but the ZSS players always got far more mileage out of them, even though they were very nonrandom. If you chucked 3 suit parts at your partner and he doesn't steal any of them, and then your partner randomly gets a green shell on his side, he throws it at you, and catch it, that illustration wouldn't solve for me the mystery of whether luck and skill are intertwined in game design.
Smash's history of controversy over stage legality would definitely stand on the same side of the fence as DXV's assertion that "not all Spikes want the same thing". Stages with random occurrences have an uphill climb staying legal, but those that inject varying degrees of variety into gameplay get passionate groups both for and against.
My favorite experience with it was when I got to pick the stage against a large-stagelist-leaning player who is more competitive than I am. I picked a stage with a super low ceiling, because his character was particularly susceptible to ceiling-kills, then I picked the best ceiling kill character, even though I had almost no experience using that character. You could definitely say I am "unskilled" at that character, and my opponent stuck with his main. And I beat him, and asked if losing that way made him reconsider his position on the stage. He said no. At the time I thought his opinion was weak in some sort of objective way, but nowadays I have a different view on it, people have their own definitions of what feels competitive to them.