The XNU kernel has great network filtering capabilities, and any modern OS can filter traffic on the kernel level. Apple could force all third-party browsers to use an entitlement that simply designates them as a browsing application, and then extend the firewall/screen time rules to those apps. It's not rocket science, content blockers have been doing this since the early 2000s.

iOS Parental Controls already allow restricting app installs. Apple could easily add an additional option to restrict installing third-party web browsers while allowing other types of apps to be installed.

I'm not willing to give Apple a pass on this major issue just because they'd have to slightly rework their Parental Controls.