That seems like part of what Brave is trying to do with the BAT: Use BAT split among websites based on the amount of time you spend on each site.
I'd rather see a self contained library that allows websites to easily insert a button which lets you tip 0.02c or whatever to them with a single click. No idea what you'd need to do to create something like that, but it seems like a really compelling way to get people to spend on sites they like. A tiny amount of pennies sent via crypto with the press of a single button could be a sizable stream when you've got scale to it.