As a thought experiment, i've wondered what would happen if webdevs started to add those ugly "This website does not support Chrome, please install [Firefox](...) for the best experience."
Does Chrome have the branding to sustain it? Would the websites take the traffic hit? If trends continue as they have the last 5+ years, it may be a test worth running.
I don't think sites want to risk losing users because of the the browser they use. Competition is brutal out there.
I use Chrome for exactly one reason: adding shortcuts to websites as an app. Firefox at one point had (very broken) support for this, but they've since removed it (on desktop, it's still possible on the mobile app).
It is simply untrue that Firefox gives me the best experience. If you're going to block Chrome because of web privacy ideology, then just say that. Don't lie to your visitors. Telling me Chrome "isn't supported" is obvious hogwash. Instead you should tell me that you have blocked it, and why you have blocked it, and maybe then I would consider opening your page in another browser.
Strong arming users with false pretenses is deplorable, no matter which side is doing it.
That's one of the most unique reasons for keeping using certain browser I've even seen.
It is a much better user experience. With things like Gmail or WhatsApp Web I don't want them to be another browser tab, I want to be able to switch to it and control the windows with my window manager. I am never closing these windows, and trying to find them among open browser tabs in different browser windows is not fun.
Browser tabs are a not a good replacement for desktop window management.
Every student in America is running a Chromebook. Why do they need branding?