However, after using up nearly a whole box of digital bandaids, like this one, which required rooting the phone, and this one, which was necessary to fully goad the still groggy N4 into reliably responding to push notifications when on wifi, well, the phone sort of works on wifi as you would have expected.
All this being necessary because Google just can't muster up the wherewithal to push out a fix for the buggy Qualcomm wifi driver.
However, if you dare to attempt to use wifi and bluetooth at the same time, say, to make a Skype call while using a bluetooth headset, boom: bluetooth kills the wifi radio. Every time. Usually locking up the phone in the process.
Other than that, the Nexus 4 is a great phone. I guess.