Now that PLA has shown us the cusp of what a catching / exploration centered Pokemon can be like, I think it would be enjoyable to theorize what a battle centric game would be like.
For me, it would of course have to include some sort of facility like BF or PWT, but I think the region itself would have a singles, doubles, and even triples campaign available to play or at least a mix of battles spread throughout the region
You would have a normal post game facility, but also bring something akin to medals back from BW2. Medals could be earned for beating bosses with certain team compositions for example, similar to how PLA had progression based on catching mons.
There would be a heavy focus on team building and battling but it would not be a stadium game.