I see no reason why resigning should be available unless it's your turn. That was how it was implemented on Isotropic and I can't remember anybody ever questioning it. I can't remember how it was implemented on Goko/MF.
Resigning should of course be possible, but I see no reason why you can't wait until your turn to do it. The biggest problem is the following: It seems it's becoming more and more common to resign in the last turn if your opponent is winning, often just a few seconds before the game is finished anyway. I think it's common courtesy to let the winner finish their last turn. The other side of that is that the winner should do it in a timely manner; but in a game of usually 25 to 50 turns in a two player game (counting each player's turns), one more turn of normal length (or actually whatever is left of that turn at the point when you feel like hitting the "resign" button) hardly matters in terms of time, and doesn't give you the right to cut it short. It's usually just poor sportsmanship and/or annoyance.
As for resigning mid-game, the same applies in terms of time: Waiting half-a-turn more before resigning does not make a difference for you. Although I've gotten used to it, it doesn't always feel nice to be interrupted in the middle of your play. The main reason is the resigning just before you're about to lose though.
There is a drawback to incomplete games in general. You never get to see how your strategy worked in the endgame, or how your opponent's strategy worked. You never get to learn how to *play* your strategy in the endgame. Your opponent just assumed (rightly or wrongly) that you would play it well and win, but you never got to try and see how it worked out in the end, or how close the game would have been. Dominion isn't just played to determine a winner and a loser, but to actually try, you know, playing the kingdoms - against your opponent of course. That said, I get that it's no fun to continue playing when you feel like you have no chance, especially if it's early in the game already, or there's no end in sight. As it gets close to ending, I feel like it's good sportsmanship to see it through - but you can't regulate that: either there is a resign button or there isn't. But there is one easy fix to avoid people resigning during the last turn of their opponent: Making the resign button available only on your turn.