Many Joomla components with registration - like Kunena, JFBConnect, etc - use normal way for URLs. Only CB not have option for nomarl URLs.
There's nothing abnormal about the URLs. It's just 2 different ways of supplying the header URL.
You can add option use "normal URLs", like in other components? (without use "live_site" for URLs)
I've no issues implementing a parameter to enable relative pathing for headers.
forge.joomlapolis.com/issues/5271
Because, Google does not agree with you.
You're reading into the suggests too extensively. They're not requirements. They're just suggestions. Both relative and live pathing work perfectly fine.