> I'd much rather have say a badge in the address bar of the browser (similar to the https badge) saying a site was gdpr compliant and used cookies

This would also be much easier to implement. Just add a GDPR-Compliant header (or similar), and the browser already knows if there are cookies.

I think the actual issue is that browsers are open source/non-commercial things that are usually owned by companies in the US (a place where EU laws do not directly apply). They would have to ask nicely instead of making it a law.