Loading quickly would be helpful. However, there are some other issues with turn-based replay vs showing current state. In games where one must choose a card to be added to a hand (rather than just played), the choose window stays active or the hand displays an incorrect card (Race for the Galaxy, Sobek, and Tournay do this). Any informative messages that are displayed as banners instead of in the log also show up for the entire game during turn-based (Pylos "You can move a ball up"). If these were fixed as well, I would see little difference between a faster load for last move and just showing the current state. If not, I would like an option just to load the current state.
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Edit: For images of what I'm talking about with incorrect card, see newly reported bug 1727. Or,
http://imgur.com/a/iTUum/all