The enormous variety is absolutely a strength, but can also be a weakness. When my daughter was a baby, my partner and I used to play a lot of Dominion with another couple who had had a child around the same time— it worked well as a quick, easily-interruptible game that could mostly be played with one hand as needed.

Initially it was the Intrigue base game (theme: cards with choices) and Prosperity (theme: treasures with side effects) and we played probably several hundred games. But later on as the other couple got more and more of the expansions, the game became less and less balanced— even with just Seaside and Hinterlands added to the game, it would have required significant study of all of the additional cards and their effects in order to have any hope of forming a coherent strategy on each game. And since that time several more expansions have come out [1].

Is this bad? No, not necessarily. Obviously if the various modules are stored separately in their individual boxes it's easy to just play with the cards that everyone at the table feels they have a reasonable comfort level with. But I think that feeling of being overwhelmed by the possibilities did ultimately lead us to playing other, more self-contained games like Agricola.

[1]: http://wiki.dominionstrategy.com/index.php/Expansions