There seems to be some tremendous confusion here. The vast majority of Alexa-family devices perform no local processing except for the activation word ("Alexa"). I didn't even realize that some of the more recent devices supported an opt-in for local processing.
This kind of makes sense, at least to me: local processing will always be limited. The entire premise of the original Echo devices was that all the magic happened in the cloud. It seems like not much has really changed?
Most Google devices do parallel local processing and cloud processing.
The local processing has less latency and works on unstable internet. It's perfect for tasks like 'set an alarm for 8am', even if offline.
The remote processing is good for better accuracy of complex words and queries.
The results are combined in the UI, making the whole thing feel less leggy (although IMO it still feels laggy to have to wait 1-2 seconds after asking a query to get results).
This kind of makes sense, at least to me: local processing will always be limited. The entire premise of the original Echo devices was that all the magic happened in the cloud. It seems like not much has really changed?