The way you see this working is purely the way the menu UI has been written.
The way menus are structured in the database allows for all sorts of other possibilities, which anyone could make a module to do.
I assume (I don't know because I was not involved with the building of the menu module and I have not ever investigated this):
The reason is that in drupal the menu UI centres around menus, not menu items.
This is because you generally have one or more menus that you want to display around the site, so you add menu items to a given menu.
The alternative is that everything revolves around menu items (paths) and you go to a path and say "I want this path to be in all these menus".
I would say the decision was made (if it was even a decision. It is quite possible it was just written this way and no one questioned it) based on perceived use cases.
Personally, I can see more use cases for managing menus at the menu level than at the menu item level. Rarely would I ever want to see all menus that a menu item is in. Usually I just want to manage a menu, then put it where it has to go in the layout. It is a discrete menu, so it is managed that way.
I can see there would be some use cases for seeing all menu items for a given page, but I definitely think it is less common than wanting to see what menu items are in a menu.
Views has menu item support so it is very easy to create a menu item view that would present the alternative UI.