Sure, you can convince people to use Firefox and drop Chrome just like IE was dropped back in the day but back then there wasn't a strong incentive to websites to prefer one browser over another (other than convenience).
Here's what I think is gonna happen:
- First the feature is added to Chrome as it is now. As they described they add it with some kind of hold-back or limiting constraint to reduce the outrage until everything is ready.
- Then the media people (Netflix, Hulu, Disney, YouTube...), who have long been salivating for something like this, push the other browsers to implement this. You really only need to convince Safari, as Edge has such a low market share in comparison that they will be forced to fold or be irrelevant (and it's not like Microsoft hates this feature anyway). For reference, Chrome, Safari and Edge make up 89% of market share. Edge alone is only 4%.
- Once the browsers are on board it's time to get the sites onboard. Really most people tend to visit social media sites more than anything else, so as long as you get them onboard you don't need to do anything else, and WEI serves their interests as well (for example it would stop you from scraping Reddit).
- As for the rest of the sites you can just make Adsense not count views or clicks from untrusted users (after all that's the _stated goal_ of this project) and site owners _will_ find ways to get their users to switch to Chrome on their own. You can add a checkbox to Adsense to get it to block your site for untrusted users to make it extra easy if you're feeling lazy.
- The final strike will be Cloudflare. Right now they rely on CAPTCHA to block bots but now they can just use WEI instead. Since most of the web uses Cloudflare now you have a gateway between the user and most sites that will tell you to go away or eternally give you endless CAPTCHAS if you are using a "bad browser".
- At this point all that is left is getting Google to give Cloudflare an exemption to the hold-back feature "for the greater good" or just kill it off at this point because there's no need to play nice anymore.
I'm not optimistic. It was easy to install Firefox and remove the IE icon on your mom's computer back in the day. It's not that easy to tell her to stop watching Netflix, Disney, Reddit, Facebook, her favorite cooking recipe site...
The best that can happen is that the internet splits and the free portion of it stays large enough to be useful. (and it doesn't get DDOSed into the ground)