That's an idea I've been toying with. I still "need" Firefox (specifically, the uMatrix addon) for surfing crappy websites, but I could browse websites I trust in an alternate browser. I hear qutebrowser doesn't phone home. I've also messed around with BadWolf a little, a very minimal browser that doesn't depend on Chromium or Mozilla and has buttons to toggle allowing JS and images, which is nice.
ZeroNet sounds interesting but I'm not sure how I feel about storing other people's website content on my PC. Sounds... potentially quite messy, legally speaking.