Hmm, I know Live probably doesn't allow an easy way for there to be persistent Minecraft worlds but it is a little bit disappointing that there isn't some way of providing persistent worlds. There are certainly other games on Live that do actually use servers, after all, albeit none that hold changeable worlds. Perhaps it is an issue of the cost of running these servers being well beyond the Live subs or the 1600MSP price point.
I was even hopeful that they might do something like Total Miner: Forge, the 240MSP Indie MC clone that allows you to save your world and send it to other players. Certainly, the TM:F worlds are not all that big, although they do go rather deep, and I'm not sure if the people you have sent your worlds to can send them back to you, and even if they could it isn't a clean or persistent way of keeping worlds synchronised if you are sharing with more than two players.
I might look to see if my aging, noisy PC can run Minecraft after all.