I think it's easy in theory (and probably hard in practice) to solve this problem. Google just needs to reduce the friction of web searches. I think they've gone a long way to achieving this goal on Android 6.0. For the uninitiated, they added that weird hold to search which automatically picks stuff out from the screen to search and often presents results in a way where it's really easy to switch back to what you were originally looking at.
Imagine if all you had to do was think about something to initiate a google search. Okay, that would probably get pretty dystopian but it would let you do many more searches even while your screen has been abducted by an app.
I think all google needs to do is reduce the frictions to search.