This is nice in theory, except the amount of fragmentation in 2020 is huge.
The average user simply cannot switch browsers.
The likelihood of encountering a website that breaks even switching from Chrome to Firefox is too much for any normal user to want to bother for just these purposes. They'll switch back the minute they find a website that doesn't work in their new browser, if they even get that far.
So unless you're suggesting "Chrome should make it more obvious how to clear cookies automatically and/or not accept them at all" (which seems like quite a UX challenge itself), saying "just tell everyone to switch browsers" just isn't going to work I don't think.
EDIT: to finish the thought -- yes I agree, browsers should provide users with choice, and switching browsers should be available to anyone who is unhappy with the way their browser treats their data, but that can't be the only way -- otherwise, the average user will get left behind.