This is my personal model for console Pokemon - something restrained mechanically relative to these MMO fever dreams but which would give the impression of a grand adventure ala my memories of the cartoon and my nostalgia for the old Pokemon culture, which through watercolor art, down to earth style, and a hefty dose of mystique, helped to conjure an image of a whole 'nother world, tangible and packed with new places and creatures to discover. Scale, interaction, freedom, from a close up, behind the back, third person perspective;
The region needs to encourage journeying as its own reward, as opposed to the tired and vapid satisfaction of defeating easy gym leaders in succession, which I feel marginalizes Pokemon a bit, putting its focus and progression entirely in combat and pushing the rest of what Pokemon is to the background. I envision a region with more than eight gyms, where gyms are shaped by the places around them and aren't always centered around straight up battling (i'm talking quizzes, puzzles, Contests, outside tasks, etc. emphasized on an equal level as battling), whose routes, towns, gyms, etc. can be tackled in a non-linear order.
Some of this could be enabled by a League Level - as you defeat other trainers and gym leaders (traditional Pokemon turn based battle system, no changes there), your trainer levels up in rank alongside your Pokemon. Other trainers and gyms will use different teams or teams at different levels depending. When you're searching for Pokemon, you can toggle between that area's normal selection of universally low-leveled Pokemon, or League Eye, which causes you to encounter higher-leveled variants more appropriate for your League Level.
Tall grass is an odd place for 80% of the world's creatures to all be hanging out together in. To make Pokemon encounters more natural and to make the ingame world seem like a more natural and organic place, the third person viewpoint is preferred. Encounters would still be mostly random when traveling through tall grass, but there would often be side opportunities to encounter Pokemon that appear in the game world - like Metapod hanging from trees along the Route, low-flying Taillow, a suspiciously gray rock in the path that turns out to be Geodude, bugs and bats on a high cave ceiling that attack when you walk under them, etc. etc. I'd want there to be lots of this, as much as humanly possible. Maybe even setpieces, like at one point you're adventuring through a tunnel and an Onix just busts the fuck through a wall.
HMs need to go entirely, to be replaced with something more Pokemon Ranger-esque - just take shitloads of existing moves and abilities and make them into overworld moves too, with overlapping effects (Cut = Slash = Fury Cutter, Swim = Aqua Jet = Levitate). You could still block certain activities, like cutting trees, moving stones, or swimming based on League Level or number of gym badges, but they should be rewards meant not to open previously blocked progress but to enable more exploration and secrets around the world as you obtain them.
The Pokedex needs to be important! It needs to have all these little details about all these Pokemon, unlocking little bits more the more you see them. It needs to be something you want to use to learn more about these creatures. Tap Nincada's wing after seeing Nincada a couple of times and it tells you a little tidbit about his wings;how they work;how he cleans them or what the fuck ever, just little details that lend more to the idea that you're some sort of pioneering explorer learning about Pokemon.
No arbitrary ass evil 'team' mucking things up. I understand the plot needs something to direct it - what about something like a looming natural disaster which forces humans and Pokemon together, or an annual tournament in the region, or just the promise of filling up a more substantial Pokedex?
Multiplayer matchmaking could be further refined through League Level and you could even have a second, compartmentalized online 'region' where trainers could walk around and challenge other trainers of the same level.