Try installing Chrome/Brave/Edge on iOS. They'll suggest setting them as default, and kick you to the Settings app. It's supposed to bring you to the Chrome/Brave/Edge app settings within Settings.app, where you can set the default browser; but 50% of the time, it'll fail, and will just open the Settings app without bringing you to your browser settings (you'll just be staring at whatever you were last doing in Settings.app, whether that's iCloud settings, manage storage, whatever you were last looking at). That bug has been there literally since Apple introduced default browser settings on iOS; maintaining it is clearly deliberate.
It would be great if Apple built an identical menu to Google's into iOS when it detects multiple browsers are installed, and let users easily choose their default browser. Even better would be Windows XP-style "browser choice".
Because they give the user choice?
Again, this isn't just a problem with the "default browser settings pane". The first time an iOS user clicks a link, the OS should give them a list of all major browsers (like Windows XP was forced to by the EU) so that no browser is favored over another. That would be fair.
Google's browser menu isn't a response to Apple's unfair default browser setting practices, but to Apple bundling Safari with iOS and unfairly advantaging it. Platform owners' browsers should ideally not be inherently favored, regardless of the platform's marketshare.
As I said, the UI iOS provides should be fixed (including a selector when the user taps a link) but at the same time, Google should not be able to use the install base of its various other apps to bolster adoption of Chrome.
That's like saying gay people can legally marry in Saudi Arabia, they just have to marry people of the opposite sex.