The practical impact of such a change, even if it were forced top down by Google, is nil. Nobody outside a tiny minority of geeks treats free software as a selling point.
Obviously not everyone would use the safe version because of the network effect of Google's play store. But for anyone who becomes aware of the "safe app store" and is aware of privacy risks, they'll almost certainly chose to download their apps from there.
All the more reason that things should be free software with anti-tivoization, so that the stock ROM on phones can be replaced easily. Most of android is free, but because it allows non-free parts (drivers, etc), it's a complete mess for people to tinker with devices because the method is different for every model.
You shouldn't really need root to selectively enable permissions for some apps either. The "all or nothing" approach to permissions is a poor design choice.
Overmore, your claim
> Nobody outside a tiny minority of geeks treats free software as a selling point.
is wrong. Just to give one counterexample, the European Comission is not a bunch of geeks and they strongly prefer free software.
The EC is a statistical anomaly. One agency out of how many out there?
I don't believe that. I think there would likely be a small group of people that would audit the software to create fact finding reports and others may create patches to fix software. Of course this is still subject to abuse, but there would probably reputations for certain sources.
Similar to journalism. There are a lot of first hand sources out there but the average layman does not read them. They would rather read a summary/interpretation of the facts. This is also subject to abuse. Reputation is important.
A “paper trail” back to the contents of our gadgets that can be audited, and some people would no doubt, would be much better than
“Fu society we own it all.”
Open source is the means of production today. Let’s keep it that way.
As that applies to the specific example in your comment, (1) people can verify whether or not a piece of open source software is listening and phoning home, (2) if it is spyware, a different programmer could make a fork and remove this antifeature, and (3) if they published the fork, now end users have the choice of using a version that does not track you.
Does this mean Open Source software never tracks you? Of course not. But it is much more resistant to this sort of thing.