I agree a good story would make it a much richer experience, and maybe to face the Elite Four of a certain region you would have to use their regions pokemon. eg. kanto; the original 151 etc
This could be implemented by some sort of story(Rules set by the Elite Four or some sort of pokemon governing body) and after you beat the Elite Four from every region you can enter into some sort of pokemon battle world cup where you can use pokemon from any region and you face trainers with pokemon over level 100 (not too much over or it would be too hard). Maybe an endurance battle where you go up against infinite trainers back to back and you see how long you last(limit potion use etc)
There is a lot of things they can do as far as stories go, I think a totally original story seperate from the other games would work best. Maybe set like 20 years after the other games or something.
I get what your saying about the regions getting repetative but I think a good story could go a long way as to not make it seem repetative, but at the same time if you play all the games back to back what you've described is essentially what you do.
Finally your point about the elite four and champion being too easy, thats always been the case. There is nothing stopping you from getting all of your sqaud to level 100 before you face them in any of the games, this could be changed so they adapt to your level. eg the better you are the better they are(level wise). Or they could leave them as they are and make them slightly harder each time you face them, they would have to be limited of corse.
Also with regards to the story, it doesnt necessarily have to have anything to do with the leagues and elite fours. It can be completely seperate so you can do all the leagues in all the regions without doing any of the story, but if you dont do the story then you cant catch any of the legendary pokemon or have certain items(like the best potions/berries etc).
The addition of side quests that dont effect the main story directly would also add to the experience. (I'm not sure if they've done this already in the latest couple of gens as I havn't played them)
Personally I love freeroam games where I have the option to do what I like and play the game how I want to play it. They really could do so much with a game with all the regions and all pokemon(pokemon over two/three versions), I think it would be a MASSIVE hit and be one of the best and highest selling pokemon games ever but once again they have no reason to do it as they make stupid amount of money from what they're already doing.