There's a "strategic breadth" to dominion that stems from it's randomized kingdoms; even with just the base set its incredibly unlikely to play the same kingdom twice, so to get good you have to consider the pairs of interactions of loads of cards. I'm not as convinced that dominion has a similar amount of "strategic depth", in that one kingdom would generally get boring to play in less than 5 play thrus as a decent player. Chess is a good default example of what I mean from strategic depth: there's a universal starting point but it can handle tens of thousands of play thrus while still being interesting.
Did you intentionally aim for (some form similar to my definition of) strategic breadth over depth because you think it's more valuable for board games? Do your favorite games generally have some form of "arbitrarily large number of starting positions"?
So far the distinction you're making between "breadth" and "depth" just seems arbitrary and negative to me. Either I'm having new experiences or I'm not; either I continue to find ways to improve or I don't. How the game achieves that seems unrelated to whether or not you have it. I mean. It's like you're saying, my games aren't as good, because of the particular ways that they produce new experiences. "Depth" is a term other people use, it will mean something to those people separate from whatever you may mean by it, and no amount of quotation marks changes that. When you say you don't think Dominion has strategic depth, you are telling those people that it sucks, regardless of what you actually mean. FYI!
I try to make games that produce new experiences repeatedly; often that involves varying starting conditions, often with those elements being rules components, to the point of "it's a different game each time." That's not the only way to get new experiences; you can for example simply have lots of designed space, such that it takes players a long time to see all of it. That's a basic thing computer games often do. You can push psychology or creativity such that you're exploring yourself or the other players; for people who like those games (far short of everyone for either category), that can keep a game replayable for a long time with nothing else backing it up. I've done some of each.
I can also enjoy a game that just gives one experience though, if I like that experience. For example I still sometimes play Boggle. Boggle is an example of a game with variable set-up where grouping it with variable rules games like mine is just hugely misleading; the variable set-up doesn't stop it from being the same experience every time.
I hold Chess up as an example of what not to do. It's too hard for new players to even see legal moves, let alone make good plays. It feels like if you were good enough you could see lots of moves ahead, but you aren't actually able to do that; so it feels like the game is telling you how stupid you are.
And yes also "explore what happens when the first 8 moves are the same but then things try somehow to get interesting" is bad. Bobby Fischer - wikipedia says, "Many consider him to be the greatest chess player of all time," and gives citations - didn't think it was so great memorizing openings and exploring those paths, and advocated randomizing the starting positions. As if then the game had more uh well let's not call it depth. More something.