I think there are a decent number of players who would like to have this as an option. My impression (based only on playing IRL with friends) is that this desires goes down as one gets more experience playing the game.
Yes, it's frustrating to have your opponent win when she has just had that extra move, and you could have won if you'd been allowed that catch-up move. But for me, that is outweighed by the benefit to the game of this strategy. . . when I play a game and I go first, I often (totally depending on the cards that were dealt, of course) play quite differently in the last third of the game. I certainly know not to play for a tie. Whereas, if I go second, I'm perfectly happy playing so that my opponent ends the game on her turn and it's a tie...I win that game just as much as if I beat her by 30 VP.
I will note that, in the Renaissance release, there is a Project "card" a player can buy ("Fleet" for 5 coins) that *will* give him an extra turn after another player ends the game. That kinda, sorta, gets you closer to the option you want.
(Since all you're asking for is an option to have this in your games, I'd support that...as I do for pretty much all options--since each player can enable or ignore. The game's creator is not a huge fan of adding all these options, I think . . . my impression is that he'd prefer people to add all these things to their IRL games. So, I'm not sanguine about your chances to have this option added. If the rumors about Shuffle losing the Dominion license are accurate, then I am sure Shuffle will not spend the time and money to add it at this point. Alas.)