Nest can't really act as a server for anything; it has insufficient power supply, probably under a watt. It can't even run its own tiny LCD screen on the power supplied by HVAC wiring. It uses that to charge an internal battery to run the screen when needed, and otherwise only partially wakes to poll the network occasionally.
Good point, though I'm not sure how often a server needs to operate yet. I suppose I wasn't suggesting that Google should abandon the cloud and put servers in people's homes -- if anything, Nest has a pretty Google-ish architecture. We all know that Android with wifi and BLE is Google's most likely "home server" at this point -- that and whatever Nest comes up with next, including those more powerful smoke detectors.
