Just spitballing: what if they rented compute based on sandboxed access to the huge trove of behavioral and activity data they have on their users (which amounts to everyone who uses the web)?

It would be the ultimate differentiator. The only potential competitor would be Facebook, who doesn’t offer cloud services.

It's next to impossible to do this at scale while maintaining user privacy.

There are some differential privacy techniques which might help, but so far they're rather hard to use and there is no tooling for such things.

The United States has no data protection laws to speak of (over this kind of data). Renting/selling access to run queries over this sort of data is entirely legal. All it would take is another half dozen years of our society continuing to move in the direction it has already on privacy.

It may just be de jure legal though; I bet it would be shown to be de facto illegal once people started mining data from federal judges and legislators...

The trick is to not care.

They do. its called AutoML.