I really want to experience a happy medium between the barebones minimalism of Gemini and the insane free-for-all of the mainstream web. In my mind, there is no reason for every website to dictate its own layout and appearance when 99% of sites could be broken down into procedural elements that could be rendered however the client preferred.
I recently bought a Kobo ereader, and the gorgeous, text-focused, crisp design of the OS is what got me thinking in this direction.
The existence of Reader Mode in Firefox and Chrome points to a common understanding that, for articles anyway, most of the web fluff is totally unnecessary. Imagine Reader Mode, but maintaining navigation and slightly more complex layouts. There are plenty of extensions that allow you to theme specific sites, but I haven't found any that try to create a unified, pleasant experience from the current chaos.
As usual, the ad-based web can be blamed. The argument that it is of utmost importance to preserve the ability to make this button 5px bigger than the other, rounded, and blue, only makes sense if you're an ad-based company trying to manipulate people into specific behaviors. By leaving the design client-side we would enable experiences tailored to providing the best experience for the user.
I don't know if or how we could ever get there, but it seems to me that mass adoption of css and Javascript in the majority of websites was a mistake, when most sites could easily be built of a much simpler set of standard widgets. This need is currently filled by pages hosted with hostile third parties like Facebook, or middleware editors like squarespace.
This kind of framework would also give online privacy to all in one fell swoop. There is no reason browsers need to be finger-printable. The reason they still are is because the company for which this state of affairs is highly lucrative is also the company making the leading rendering engine.
Perhaps what I'm actually asking for is a splinter net, or maybe something like this is still achievable by just parsing html.
While I relate to OP's fed-uppness, building a browser seems to me like trying to play catch up to a system that will never have your interests at heart. Not that I think the project isn't worthwhile, it just triggered the above thoughts.