The best pure browser company in history was Opera, and they didn't fail because they weren't innovating. It is simply not a survivable model. People don't remember anything, but during Google's recent anti trust case, one floated "solution" was to spin Chrome off as a separate company, but that was regarded as unrealistic partly because such a company would not have a credible path to profitability separate from Google.
I happen to disagree, they could have collected a search licensing fee just like Firefox but that model is already being regarded as monopoly adjacent.