I suppose one could do this but then each OS will have to set flags on the browser executable and there is a whole can of security worms that opens. In Linux one could use
sudo setcap cap_net_raw,cap_net_admin=eip /usr/lib/firefox/firefox
If using AppArmor or SELinux rules would need to be created unless Firejail is managing the rules on the fly. Then the browser would need to test for the capabilities and give some meaningful log in the web console because a way to debug this is considered good ettiquite. Then one would need a library or API in the browser that knows how to open raw sockets which means getting all the major browser developers to agree on a standard.
Thinking long term there are going to be security auditing tools that will detect the binary has non standard setcap modes meaning that browser developers would have to reach out to all these companies to get on the same page otherwise corporations will have some knee-jerk reactions.