It’s a cool idea, but it wouldn’t work in practice. There can be multiple properties editor and outliners so it’s impossible to define when a tab is selected and the icon should be shown highlighted.
If you haven’t seen the UI team meeting notes yet, we decided on a solution for outliner to properties tab switching that I think will satisfy everyone. It’s working well already in this initial state.
Each properties editor has a popover menu for settings. A dropdown (defaults to auto) can be used to set the properties sync behavior. Auto is the shared edge behavior which works for most cases, but when you want to enable it or disable it always the option exists. I think this small patch can get reviewed and merged this upcoming week 
Thanks again for the feedback on this feature!