I imagine unreliability of home networks just makes this a bad idea for things like email even if you somehow managed to get around all the other obstacles like security/privacy/trust issues (spam, etc.)
But all of this is separable: storage at home, transport/computing provided by Google. So security and trust verification can come from Google (or any other provider) but emails stay home. Or photo processing provided by Google, but photos stay home. That would however relegate them to a pipe and service provider and possibly force them into openly competing, so they would never do that. Owning your data for the lock-in is the point.
