Ironically, we already had that - Microsoft's first version of Edge was using their own engine. On release, it had the highest W3C compatibility score.
Google started shitting on it (including things like serving clear HTML version of Gmail because "the browser is outdated" if it detected the Edge user agent) and massive self-delusion campaigns of "Edge is just Internet Explorer" eventually killed the thing and forced MS to switch to Chromium.
I have Ladybird installed and I check it out every now and then, but I honestly doubt that a bunch of random developers will succeed where Microsoft failed. Unless Cloudflare somehow chips in and forces Google's hand into compatibility, but I don't know if even they are big enough to do that.