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It probably wouldn't work very well with the undo feature in effect.  However if there's no do-overs,  like in tournament chess,   it might work.

It has been mentioned in the past that there may be a no-undo option available in the future.   Still waiting for that.

Ingix - it's because it *feels* rude to deny undos manually - and often provokes players to be abusive in response, no matter how much we hold the principle that undos are optional. Undos on/off as a matching criteria would avoid this social difficulty - as it established the attitude towards undos before a player commits to game.

I intend to build this feature, but I am also afraid you will be very disappointed by the results.
I have a feeling that selecting "I only want to be matched with people that never allow undos" will turn out to be annoyingly close to "I like to just sit & wait here while not getting matched". The people that at least want to allow some undo's are an overwhelming majority.

Look forward to this being implemented.  I believe at least a significant minority of players will choose the 'undo off' option so that it won't be too hard to find opponents.  It could result in 2 sets of players (those who want the undo feature & those who don't) that rarely or never play each other,  so a player with a rating of 50 in one group might be significantly different in strength from a 50-rated player in the other group.  Since some players who like the undo feature often use it to get around the rule that you're not supposed to look ahead in the deck (see rules to the base game),  a player with a rating of 50 in the no-undo group will likely be stronger than than a 50 rated player in the pro-undo group.  Speculation, i admit,  but it could have implications in tournaments if people are paired / classified based on their ratings.
The undo feature is kind of like a demagogue politician,  it divides the community.

A stronger bot(s) would be great,  I prefer playing bots due to their fast play & because they never ask for undo's,  but the current bots aren't very good & have known specific weakness.  The best chess & backgammon bots are at world championship level,  this  should be possible with Dominion.
Ideally there's no undo feature.  I really resent being presented with an undo request that reveals future information (honest mistake or not) & having to decide whether to allow my opponent to 'cheat' (because they looked ahead),  or deny & face verbal abuse (my blacklist is full of such players).  It should be automated where some requests are automatically allowed,  & not being allowed to even ask if future info is revealed (including asking when it's not your turn).  Going back multiple  steps seems ridiculous,  why not go all the way back to the beginning of the game if it's not going your way?  That stuff should be banned,  at least in rated games.
Even undo requests that don't reveal future info can be problematic:  victory cards with multipliers (Feodum, Silk Road, Gardens) can cause the victory pt total to drastically change when certain cards are obtained,  also some of the Landmarks (Keep,  Orchard, Palace) can have this effect,  these could prompt an undo request if the victory pt total doesn't change  as hoped.  Should this be allowed,  esp if it's maybe the last turn of the game & may make the difference between winning & losing?  If an undo request is denied in such a critical situation,  fair chance both players end up on each other's blacklists.  If there's no undo feature,  these  events that cause strife & bad feelings don't happen.

Coming from a chess background (no do-overs in rated chess games) I don't like the undo feature.  I've never asked for one,  and never allow it if asked for after cards are drawn or future cards viewed,  I usually allow it otherwise unless the opponent asks for it excessively.  It's definitely the cause of a lot of strife and I'm sure that players' blacklists are much fuller because of the undo feature. 
In my opinion,  Dominion is the best game invented since Chess,  it's so subtle,  there is some luck involved but skill plays a much bigger role.  I think the undo feature does somewhat of a disservice to the game,  there's kind of a pervasive do-over mentality.
In a rated game,  my objective of course is to win if I can,  not to help my opponent win.
I know that a lot of players don't like the undo feature.  Perhaps a poll should be taken on whether players that play here want the undo feature or not. 

That's happened to me twice in 3 player games after one of the opponents resigned (resigned in both cases,  not disconnected).  If playing in a game with more than 2 players,  all players should finish the game.