They'd probably be fined into submission if they don't though.

If it gets to that point, one alternative would be creating some ad-hoc non profits that are on paper not controlled by them (but in practice they are) and then giving up the control of their respective browsers to said non-profits.

But it won't get to that point. I don't really think the US government would be ok with a regulation like this, either, and they have even more bargaining power than tech companies.

You think the EU's lawyers will be fooled by a scheme you cooked up in an HN comment?

then the non-profits would be breaking the law

It's a market of nearly half a billion people, two-tier browsers seem more likely. IIRC Netscape did this in the past over US export laws on cryptography.

Developing a browser these days mostly involves slapping on their own branding over Firefox or Chromium though, so hardly the end of the world for EU.