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Fan-wise: Gewunners, 'nuff said.
Game-wise: My main problem is that lots of decided improvements to the game are one-offs or never get follow-through.
We have a whole game with custom trainers and now they're gone. I hope they return in gen 7 but who knows?
For further examples, BW2 had Memory Link, the PWT, and the beloved Challenge Mode. Imagine if GF actually followed through with Memory Link and had a battle against your team from BW1. Battle Frontier and a PWT equivalent are notably absent from gen 6. Finally, Challenge Mode was a step in the right direction but again is gone with the wind.
A lot of system design could use an overhaul too, and I don't even mean something crazy like switching to a real-time system or whatever. Imagine an easier EV system that spelled everything out for you. Instead of focusing on particular species, hordes, or minigames, let the player explicitly dictate Pokemon growth. "Your x leveled up! Please distribute stat points!" Many other RPGs already did this so the idea of gaining specific EVs from specific Pokemon just seems like a relic of the past rather than a defining feature.
Moreover, with all the advances in breeding, which ORAS did improve with having the second daycare, Judge, and and infinite loop on one island, let's just streamline it from the start instead of sidestepping earlier design traditions and flaws. Why not open up a user-friendly menu to specify what gets passed down? Maybe let the player choose 1 or 2 IVs to get passed on and leave the rest to Destiny Knot and RNG? I get GF probably wants some randomness, so all I'm asking for is something small.
Drawing from the original monster-catch RPG, Shin Megami Tensei (and spin-offs like Persona), there you used to have constantly re-roll for proper attacks and stats, but now you can choose what moves get passed down. Why not let Pokemon give some more player-control in making their own monsters? We're already starting to do that in convoluted ways anyway.