So far, it's unanimous!
I think it'd be awesome to have a site that makes it easier to create, oversee, and participate in succession games, and that stores all the save games.
Provided, of course, that the site is inexpensive enough, funded well enough, or has a sustainable (but not painfully annoying) economic model, and doesn't go down taking the saved games with it.
I feel like the "queue of players who will play in this order" model of organizing succession games is one of the biggest problems with succession games...if you sign up, unless you always have free time, your turn may come when you don't, and that slows down or kills a lot of succession games.
To me, the biggest advantage of a website facilitating succession games would be that you could set up a game to be open access, but lock for a period when someone downloads the game file. For example, you might set up a game with 24 hour turns. If nobody's grabbed the save file, it'd be open for the next comer who has time to play right now, once somebody's clicked to download, it would be locked until either the download fails (in which case it unlocks again quickly), or the player who downloaded it uploads the results of their game, or the clock times out and the old save becomes available again.
With a setup like that, a popular succession game might see several turns played each day by players in different parts of the world, or with different schedules.
Instead of having turns set up in some particular order, you might have an allowed players whitelist (or for public games, a blacklist), with players removed from the whitelist (or added to a public game's blacklist) when they take their turn (possibly with some kind of time-out, if multiple turns by the same player are allowed, or if the file isn't claimed by a new player for some length of time).