But in the future..
As I understand it, these things communicate back to the Bezos mothership primarily for the voice recognition engine. Sure, a request to play an internet radio station or tracks from Spotify requires an internet connection, but for tasks like setting a timer, controlling the lighting and so on, it isn't necessary apart from the remote processing.
Once it becomes commercially viable to package the required processing power into the device itself, I can see them really taking off. I'd be delighted to have one central device that responded to voice commands and could do things like set an alarm, turn on the lights and draw the curtains*, but only if I could be sure that nothing, and I mean nothing, was leaving the four walls of the house.
*additional hardware sold separately