My suggestion, though, is different. If NIST has such an approval process, then, Apple/Google/Mozilla/anyone else doesn't have to go through an approval process

My suggestion, though, is different. If NIST has such an approval process, then, Apple/Google/Mozilla/anyone else doesn't have to go through an approval process, but if they do go through such process then they can put on their product, the sign "Approved by NIST as web browser compliance". However, I am not so sure that such a thing is even necessary at all. I think the use of the web browser should be reduced in order that this is not necessary.