I think async would be bad, but I'll play devil's advocate.
Even in a game with competing Torturer chains and Moats, the number of times you need to reveal a Moat during your turn is only going to be around 5. That's not entirely unreasonable, since it won't happen every turn. Sure, there are even worse situations if you're KC'ing Spies or something like that, but such games are fairly rare. No need to give up async because of those <1% of games where it's unusable.
Also, async can be thought of as a sort of auto-save. Auto-save is good. If both players are willing to accept that one player might need to take a break and resume the game later, that seems fine.
Finally, async play might ban certain cards so that you never need to make a decision during your opponent's turn. Granted, this rules out many interesting kingdoms, but there are still plenty of interesting kingdoms left. Playing with restricted kingdoms is still real Dominion, since the rules of the game specify you may choose kingdoms in whatever manner both players agree to.