What I'd want more from the features we currently have are one of these (because it's very unlikely we'd get even two, let alone more, of those) :
- More mega-evolutions. I'm not alone on this it seems. Lapras, Vileplume, Omastar, Kabutops, Meganium, Typhlosion, Feraligatr, Exploud, Probopass, Flygon, Cacturne, Torterra, Infernape, Empoleon, Luxray, Froslass, Serperior, Emboar, Samurott, Malamar, Cincinno would be my top-20 wishlist.
- More regional variants. It's hard to say which Pokémon should get one considering it will depend on the region, but I think it was a great idea and it needs to be pursued.
- More evolutions. Something many have wanted for years. I don't know why they stopped after gen IV, but some Pokémon could definitely use an evolution. Jynx, Girafarig, Dunsparce pls, Qwilfish, new EeveelutionS...
- More z-moves that are not just higher damaging moves compared to what the regular z-move would be (see the z-moves for the Alolan starters especially...). Basically, more z-moves like Clanging Scale, Extreme Evoboost, Genesis Supernova, with an added special effect.
Also, it seems like the "new feature" is always related to the regional Professor's work.
- Gen II : Professor studies breeding, so breeding was introduced.
- Gen III : Professor studies habitat and behavior, and weather and abilities were introduced. While not exactly related, you could say abilities are linked with behaviour and such.
- Gen IV : Professor studies evolutions, and several evolutions were introduced.
- Gen V : Professor studies origin of Pokémon, and a very large amount of Pokémon were introduced, as well as several legendaries.
- Gen VI : Professor studies mega-evolutions, so megas were introduced.
- Gen VII : Professor studies attacks, so z-moves were introduced. There was also professor Oak's cousin, studying regional variants (introducing Alolan forms), and the guys at Aether foundation studying ultra-wormholes (with which they introduced Ultra Beasts)
So with Gen VII introducing so many new features, I think this generation is perfect to take a break and focus on improving on existing features. Otherwise, what I think we could see are :
- A professor that studies Pokémon symbiosis and relationships, which could allow the introduction of more "linked moves" (like those tutor moves for the starter pokémon) and/or "linked abilities" (like plus/minus).
- A professor that studies Pokémon training, which could allow better control over IVs/EVs (I saw someone propose, in another thread, that we could manually distribute EVs after earning them, much like those ability/statistics points in several RPGs, and thought it was a neat idea)
- A professor that studies Pokémon evolution, which while similar to regional variants, would allow the introduction of "past forms" of Pokémon. Or fossile forms. What they were before becoming what they became. I think you understand.
- A professor that studies Pokémon fusio... Yikes, no, please.
- A professor that studies alternate evolutions, which could bring more Gallade, Froslass, etc. Evolutions based on gender, certain conditions, etc. And this could open up the way to several eeveelutions too.
- A professor that studies Pokémon abilities, which could allow the introduction of several new gimmicky abilities (even if SM had its fair share), and/or of powered up abilities (with an item, just like z-moves or megas).
- A professor that studies Pokémon bonds with their trainers, which could bring up trainer adaptation (no idea what to call this, but a Pokémon base stat could vary based on its bond with its trainer, while being separate from IVs and EVs) or even Pokémon customization (which should remain for aesthetics only). Could also introduce more "bond forms" like Ash-Greninja for certain Pokémon, with the Pokémon taking on features from the trainer.
Can't think of anything else right now. I'd love the last mechanic personnally, but would much rather that they focus on existing features, as I said.