Like on an Apple II?
https://web.archive.org/web/20150405004057/http://apple2info...
Check out Geminispace https://gemini.circumlunar.space - one of the design requirements of the protocol is that it be simple enough that a single person can implement a browser for it in a weekend.
I'm not sure, just for the fact that the best browser is something that could vary quickly, there might be niches, different native versions...
Cross origin caching of resources is a privacy risk
If site A can tell based on timing information that you probably visited site B recently, that's a pretty big privacy issue
This has largely killed cross-origin caching on the web, as I understand it
Of course there're many hard questions. For example downloading an entire JS+HTML+CSS engine with every website is not a good approach, some caching must be done. There should not be version hell with every website asking for a different version of engine. But those questions could be approached as a more general web library issues.