The solution to the "my opponent is taking to long" is to play against someone you know, or to pay the $.99 for the full version and get 5+ games going at once. Also it seems to me that in the evenings you're more likely to find people that want to play continuously.
But the "take your time" aspect is very nice if you want to have a casual matchup with a friend over the course of a day or so and not have to worry about playing as soon as they are done.
Edit to add, since Game Center doesn't support any sort of direct messaging, it would be nice if the game at least had a way to send a few pre-defined messages like "good game", "nice move", "stepping away for a bit", "sleeping", etc.