A client/extension that you can build yourself, that can report the time you use an app. Sadly, you need to reveal some data. But most can stay on device.
All that is needed is really total hour each app is jsed and calculate the ratio.
This assumes equal weights for apps, but can be changed.
You can create bundles for different content types like news vs games as price tiers.
If it is all client based someone could chose to use a patched version that e.g. donated all their money to charity. NB "never trust the client".
You will never get the big websites that monetise with advertising on board with client side analytics. That would need e.g. server side analytics or DRM on the client side app. Either way I wouldn't touch your app and nor would most that block adverts - and the big websites would probably not be that interested either.
Maybe with reproducible builds you could have a trusted build that people could build at home that also signed the requests with the analytics data. I don't think that the technology to do this exists yet.
-> Donated all money to charity: i don't see how that' possible. Money gets to the company, and gets distributed. If you wanna give money to charity, just do so, and install an ad blocker it's the same idea. You'd miss out on the premium content bundles that I am thinking of.
-> Apps and websites will do so. Many news papers (albeit a losing market in general) offer premium subscription. You are literally making that easier.
-> I do not need trusted builds. People advanced enough to do what you said already can install ad blocker. They still won't get premium content access, and clients can always choose to "verify" -> this actually will happen using public/private key cryptography.
