As of the last couple years, Chrome is the web. The writing has been on the wall since at least Widevine. The browser wars are over, and I don't see any scrappy startup crossing the moat of complexity GOOG has built around "modern" browsers. Especially when combined with their stranglehold of the standards committees. We need to find a new attack vector.
Things looked similar amid the dominance of IE. I think it will probably happen eventually, though you're right that a start-up probably won't do it. The problem that no one pays for web browsers. There are companies building alternative engines for commercial embedding (including one that's parallel and very fast), so it would probably involve one of those being open-sourced.