Obviously there is some sort of internet service needed for the device to be controllable over the internet. However, I fail to see why internet connectivity would be needed for it to work within your home network.
The app communicates with it over Wifi, and then it communicates with the various smart devices over their respective networks. Why would it need a connection to some server for that? The only explanation I can come up with would be that the device was underpowered, and processing of the different actions was done on server. But this was not some $29 gadget, it was $299 — for that price you can get a complete Windows PC. So I think it’s not too much to ask for lifetime service.
I can understand if some functionality gets disabled (like Nest thermostat support). If the whole device gets disabled, particularly if it does not even appear to be technically necessary, then that’s just beyond me. In my opinion, Nest should continue the service — or make the API open-source.