So I have a thought about the how the openness of the region and ride pokemon could work.
Open region: We know that SV is going to be open world the questions is how open. Breath of the wild is what generally comes to mind. In BOTW you can go to any section of the map from the start without anything limiting excess. If you want to go to hyrule castle, the island in the southwest, or volcano you can. Whether you survive those areas is a different thing; however, you can go there if you want. However, you cannot reach every part of those sections. You cannot climb up every mountain, swim across every lake, glide across every open space. To reach these sections you have either spend your stamina by completing shrines or craft enough stamina rich foods and elixirs. SV should use this model and apply it to it’s open region. However, stamina shouldn’t work the same way it does in BOTW. Stamina should be tied to the pokemon you are riding. SV should expand on the ride system from Legends and allow the character to register their own pokemon for their rides. Each type of ride; flying, surfing, climbing, and riding should be upgradable and each upgrade should be locked behind completing a gym. Each ride start off at level 0 and can be upgraded to level 3. For the four rides, 8 upgrades are locked behind the gym badges, and then 4 more for beating the elite 4 round out the upgrade system to 12 upgrades and each ride caps at 3. You can choose which mount you want to upgrade, if you want you can fill you surfing ride upgrades on the first 3 gyms. This would be similar how in BOTW you can choose whether to upgrade your stamina or hearts for your play style.
Rides: Each ride would have a set of pokemon that can be registered to that ride. This would be done from your rotom phone or pc. The regional bird would be the base flying example. Stage 1 would be flying level 0, stage 2 is level 1 and stage 3 is level 2. The regional bird would not reach the highest level, without help. However, if you choose to evolve your ride and you have not unlocked the next level the game will warn you that if you evolve this pokemon at this time you will need to register a new pokemon for that ride. SV would need to use Legends evolution system, where the player picks when they want to evolve their pokemon. Each upgrade improves the ride. Level 0 is the most basic for each ride, for flying you can only fly for a short time, slowest speed, a short vertical lift before gliding. Each next level has a longer and faster dash, and the vertical lift improves each time. Surfing tier 0 slowest dash speed and shortest stamina, with each level getting a little faster and more stamina, with tier 3 unlocking diving and unlimited stamina. Climbing and riding level increases would be speed and stamina based. As you upgrade your rides more parts of the region become accessible and in these new areas rare pokemon would be found and pokemon with higher tier potentials would be found as well. As a reward for being the champion, you could earn items in the postgame to upgrade any fully evolved pokemon within the ride to highest level. So you could get your regional bird to level 3 this way.