Maybe someone enlighten me here. But unfortunately it's not an easy one. Not one I can think of I would be happy with. Not one that doesn't create all the problems I'm trying to solve or stay away.
The problem with your idea is that it's not the saving and loading of the urls in the RTE but you're talking about the url field you see when selecting a page. That's the page linke editor that works together with a each PW specific RTE plugin editor on top of that.
1. So, one and easy way would be to alter the $page->url via a hook (as it is now or was), but that's where it will be systemwide changed and many things may and will stop working. Maybe some options there to only alter if-then... but believe me it creates a whole tale of issues that arise in one place or another. Mixing it up with "here you do it but there you don't" etc.
2. The other would to explore the PageEditLink module and probably only JS side to see if it can be somehow hidden, but by not altering the -in and -output. That would be more a cosmetic fix. I'm sure there would e some way or another, although not that easy. While I understand what you're saying that it creates usability issues, I think it can also create problems if you hide something that's relevant information too. Imagine you only see "/about"/ and "/about/" but which is which? We have lot of editors that edit multiple sites and cross linking should be easy. Maybe best way would be to "grey it out" and make them aware that it's "secondary" info due to multisite.
The other "problem" here is that it would have to be done for all RTE's etc and upcoming link editor plugins. And as it looks one would have to completely replace some of the complex PW RTE plugins and or the link editor js to make it work, and always try to incorporate changes and new features in the core that will occur in no time for sure (and then there's front-end editing).
So it's also a question of how deep this modules should go or stay out of the way and don't create too much dependencies.