That is an interesting idea. To go back to comparing it with chess, when watching WW's stream I will occasionally watch him play speed chess. I forget exactly what app he plays it on, but he can set the timer to 1:00, 5:00, 10:00, or whatever. It is still chess, but the game is completely different depending on what amount of time you allot for the game. 1:00 for all your turns (so 2:00 combined) is totally different than a 5:00 timer, which is again completely different than an untimed game.
Basically, I think I would really enjoy playing this way, but when playing you just have to remember that it is a completely different game than untimed dominion. Also, you have to remember that you can't just make a play in a split second. To buy and play action cards there is a lot more interaction than you would have with chess. And therefore a lot more time. And then inter-player interaction within turns would do strange things to how you keep time. And then the different cards would effect how long you need.
Ok, continuing with stream of conscious thoughts: What if everyone started at 0:00, and your timer goes up for how long you take making decisions, and your opponent's timer goes up when he is making decisions. Then do something with the total time, number of turns, dividing those numbers in some way, translating to VPs, and then adding to the overall score? I don't know.