Unfortunately, I doubt it. Chrome made it as big as it did because it had one of the biggest tech and advertising companies in the world behind it. Other than Microsoft with building in Internet Explorer into Windows, thereor Apple doing that with Safari, isn't anything else that could compete as easily, and we all how that went for Microsoft.

And it would only be harder today, since they'd not only have go contend with Chrome, but also that a lot of websites are being built around Chrome/browsers using the Chromium engine. People would go to a website that either refuses to work, or doesn't work properly for their browser and hop over to Chrome instead.

Netflix requires specific DRM addons that are really only available for the major browser engines, as an example. If someone is rolling their own, like KDE does, then that's going to refuse to work outright.