As it happens, I was taught Dominion by other players, but really learned it from online play and other such resources. It's the sort of game with depth that exceeds most players' patience - extremely replayable, but only if you don't really care about the fact that the theming is paper-thin (literally, in a sense) and happen to get captivated by the core mechanics (and the variety offered by the expansions).
This was way back in the Isotropic days, before there was an official client. So you could play games very quickly without any of the physical card manipulation at all, never mind shuffling. (It was a very minimalist client that didn't try to simulate any of that card movement with animations; it just immediately updated hand and pile contents and resource counts.)
I guess it's really just not for everyone.
(A story: years ago I tried to design my own deck-building board game which borrowed several Dominion mechanics - but you would play out your cards physically like tiles; instead of an action-counting mechanic or an Action/Treasure dichotomy, there were restrictions on what cards could be adjacent to each other. The feedback I got was overwhelming in its consistency: the more it played like Dominion, the less people liked it. But without that anchor I was lost in terms of designing something that made sense and had anything like game balance, and eventually I gave up.)
My opinion, maybe unpopular, is that if you really want to feel like you're managing a medieval kingdom (or whatever) then computer games are just better anyway. For anything that gets the slightest bit like a simulation, you want to let the computer do the bookkeeping.
But even for computer games, after you've played for hundreds of hours of say Civilization, and especially if you approach it competitively, you hardly feel like the Hittites anymore. By then, it's just an abstract game for you, and you're OK with it or you'd have quit long ago.
This was way back in the Isotropic days, before there was an official client. So you could play games very quickly without any of the physical card manipulation at all, never mind shuffling. (It was a very minimalist client that didn't try to simulate any of that card movement with animations; it just immediately updated hand and pile contents and resource counts.)
I guess it's really just not for everyone.
(A story: years ago I tried to design my own deck-building board game which borrowed several Dominion mechanics - but you would play out your cards physically like tiles; instead of an action-counting mechanic or an Action/Treasure dichotomy, there were restrictions on what cards could be adjacent to each other. The feedback I got was overwhelming in its consistency: the more it played like Dominion, the less people liked it. But without that anchor I was lost in terms of designing something that made sense and had anything like game balance, and eventually I gave up.)