Two quick comments:
Dominion, is first and foremost, a card game. It is highly unlikely that the amount of people that know how to play dominion and/or have purchased dominion online will ever surpass the amount of people who know it and/or play it regularly IRL. However, what you may see, is that people who may not own dominion, but play it with friends, or dominion fans, will add to their addiction by playing online as well. A good implementation will attract more casual gamers, but I think the internet is full with plenty of fun computer games that aren't pretending to be card games, so chances are people will find Goko Dominion because they are already know about Dominion, and more casual people will stick around then they do on iso, on account of it being easier to use. (and more possible for them to win, b/c of the bots)
I have a feeling that if someone is trying to specify 5 Prosperity cards, that they would be a little confused at only getting 1 or 2. Of course at that point, they are screwing with probability, chances are, they want to. In that case, rather than a flat average, it should be, a flat average given the constraints. So, there should be no particular prosperity card favored in the 5, and no particular non-prosperity card favored in the other 5. Tools need to be straightforward: Gimme 5 Prosperity shouldn't give me 2 prosperity!
As a note on new players:
I usually do like to introduce new players to the variety of Dominion right away, so that they can get an idea of what the game is all about. So, I do draw randomly from all the sets I have available, with three caveats:
1. I take out game killer cards, that are easy to run away with the game if you know what you're doing. This is mostly to prevent temptation to myself. For example, fool's gold, goons, (especially if there is a village), possession, tournament. For some reason people are pretty good at figuring out the value of KC or Throne Room, so I usually can leave those in.
2. I try to make it a little bit of a learning experience, so if I see that a certain type of winning strategy is more possible, I'll swap out cards to make it a little more obvious, and still possible to do if they buy things randomly.
I try to take them through four main 'flavors' of winning dominion: The engine game, the big money game, the greening game (aka special VPs, a la gardens, or bishop or duke etc.), and my special favorite, the hail mary three pile scramble (don't need special victory points, just end the game when you're ahead by buying out three piles, works especially well if everyone is trying to buy the same actions and there are lots of cursers out there).
3. I explain the importance of trashing and junking early on, and may even play a game with nothing but trashing and junking, just so that they can see why junking is bad if it happens to you, but not the end of the world if you manage it, and that trashing is powerful (even those hard-earned estates that you start with! Even if you could buy a silver instead! Nobody likes to see those go at first, for some reason). Also, I help them see that junkers, especially cursers, can be an easy ticket to a 3-pile hail mary.
Any randomizer trying to make the game more fun should probably take those into consideration, and each one separately (maybe there should be different randomizers for game flavors, or a slider?) For example, what makes an engine game can kill big money, greening could kill an engine but depending on the board the engine may be faster, engines or big money could lose to a well-timed three pile scramble, sometimes two or more strategies are possible on the same board but that usually makes the board a little weaker either way since the strategies are at odds with eachother.
I don't think its fair to prioritize one way of winning the game over others. Engines usually get picked up at first because they are easy to understand, but once people realize there are other ways to win they enjoy trying them (one of my latest games with new people ended with a tie: one person had gone big money with fools gold, smithy and squire, and bought out almost all the fools gold, the other had gone engine with smithy, golem and festival after trashing everything they started with, got almost all their money from actions and by the end went through their deck every turn, naturally. All the people playing were impressed that such radically different strategies could have the same end result).
From what I can gather, your simulator doesn't keep these strategies distinct. They are very distinct, and pull the game in different ways. Maybe rather than try to enable all of them, keep them as separate 'flavors', that could be mixed, but not necessarily.