I have always loved this idea, as I'm sure many have.
I propose that the trainer has a level 1-100 like the Pokemon to replace the badge system.
I also think they should have talents such as your
"Leadership: Pokemon up to x level to obey" but appart from that, damage up, catch rate up, specific item specialization, better at raising x type of pokemon, lower specialized type's weaknesses to avoid part of those devastating super effectives that cause a level 10 Polywag to one hit elite four level 50+ entire lineup with bubble.
You could increase experience rate, movement speed, learn toggle skills like "Tracking- Find battles more quickly while active, find battles less frequently when inactive"
There is a lot you could do with specialization like that, obviously you have trainer style reflected in them, extending to perhaps Unfriendly/cruel training being a trade for less loyal pokemon but higher stats.
You could have in game tournaments organized, regions determine your starter Pokemon, avatar flavour, and leveling experience.
higher level cap with expansions could be reflected in regions that come with a starter area and then a restriction to higher level players to enter later in the game to avoid the development trap of remaking complete territory.
Pokemon could be manipulated directly in combat to offer more tactics in kiting and dodging, providing certain types a very unique play style (burrowing, flight, slowing ice moves).
Since you are assumed to be the trainer not the Pokemon your masteries/talents could physically effect your Pokemon's stats in the form of not only training but leadership which would represent how well your Pokemon understands your command.
Quests could be shown like episodes of the anime, perhaps with anime cut-scenes to give it a nice edge in how much we care beyond the reward of some menial task. There would be the filler go collect x, and the dailies and whatever but Pokemon has a big world with interesting character that they could abuse. If we actually have an episode with a mystery and promise of pokedex entries, potential rocket thwarting, gym battles, npc heliping, and all the traditional loot/exp/money. I think it would be more enthralling then just quest text. I want to meet other trainers, a lot of that will be players, but don't cut corners and rely on that, online communities are volatile. But in some really interesting npc trainers that I want to interact with.
VOICE ACTING. I will NOT read quest text for every quest I ever take, I'll skim for compass directions and clear cut a swath of every enemy in hundred miles.
END GAME. This is important, very important, to important to stress.
It needs to happen, it's and mmo, people will leave it if they don't.
So we need some Movie quests.
Episodes aren't enough for endgame raids we need to deal with those uncatchable legendaries, we want that unatainable mark on our pokedex that says "This trainer actually saw Ho-Oh and Mew and not only that but helped solve some world ending scheme."
10 trainers invited to some exclusive island for an event that goes terribly wrong and threatens all of your pokemon.
Perhaps force the trainer to do some things without their pokemon by separating them.
Tell the story for more then one perspective and trade between trainers and Pokemon with the players working together through it.
The hurdle would be development.
It could not be half ass work, it could not be glitchy, I would not play it if it was the same sprite recycling current Pokemon games are, graphics DO mean something. I want to see anime cellshaded 3D personally. Valkyria Chronicles or Ultimate Ninja Storm, I'm not unrealistic to ask that quality in everything but a far point to strive for is good.
They need Blizzard or Turbine quality really, those are the ones I'd trust with the idea anyways, as long as they worked closely with the minds of Pokemon.
If they spend less then years and years polishing it, it will fail it's launch and return nothing and permanently murder the idea.
I could probably go on for days with this, and have before. It really is truly one of the best idea's ever.
A lot of this is likely unrealistic impossible dreaming and I know that, I'm not completely insane. Just saying with Pokemon I set a high bar, this is what I'd want, not what I think I'd get.
edit: TLDR: If some omnipotent god that exists not in our mortal plain touched the genre and inspired perfection.
Then I'd like it if it took the form of Pokemon.
I don't want some crappy typical pokemon game, just online.
I want the World.
