Probably a lot; open-ended voice recognition with no prior training is hard (though I'm not convinced it can't be made to work off-line now that the models are there). Still, a lot of devices don't need open-ended voice recognition (structured grammars greatly simplify the problem), and if you allow for users having to pre-train their devices for few minutes, off-line processing becomes easier.

My impression is that the main driver behind cloud-first voice processing is business, not technology.