These are the things I would like to return:
* Character customization
* DexNav (specially searching specific Pokemon and being able to catch them with IVs)
* Soaring
* Gym Leaders and Elite Leaders rematches
* Better post-game content, specially on the legendaries and battles part
* Being able to play with two starters
And these are the things I seriously want but I don´t think they will happen:
* A 5th moveslot. It could be just a HM moveslot. That way, you wouldn´t waste a slot on an HM and you wouldn´t change battles too much with the new slot. Say goodbye to HM slaves!
* Difficulty levels from the start. And make hard actually hard, I love grinding but on last games I can´t.
* New Game +. Let me play the story again without losing my captured Pokemon, TMs, etc!!
* More than one region. The thing I LOVED about Gold and Silver was going back to Kanto too, even if that region was a lot more empty. Now that games are on 3D, you could put Kalos or Hoenn on Sun/Moon.
* More than 8 gyms. We have plenty of types and Pokemon. Why not use them?
* All Gym Leaders with 6 Pokemon. I truly hate all those battles with just three-four Pokemon. Come on!
* Extra postgame battles at level 100. That level should exist for a reason, and with online play at level 50 and not many high level battles, it´s just a waste.
* Hard to catch legendaries. Stop being able to catch them with a stupid normal pokeball, I prefer legendary battles to be epic. A nice way to do this could be that legendaries were buffed up a little on stats, but used two slots instead of one on trainer battles. That way they could even be available on online gameplay.
* More than 6 Pokemon slots. There are 720+ Pokemon and we still have to choose 6. I would like increasing this number.
* No routes with just 1-3 pokemon only. There are so many for a reason, and it´s tiring when you get one route with mainly just Zubats, Tentacools, etc. More variety, please!
* Being able to see the IVs from the main menu. Is it really that hard to show a Rank next to each stat? Like S on HP, A on Attack, etc... If any of you have hatched chaos on Sonic Adventure you know what I mean...
* Maybe many wouldn´t like this, but a way to raise Pokemon IVs after already catching/hatching a Pokemon. I think it´s a waste not being able to raise a good IV Pokemon if you don´t hatch him like that on the beginning. I don´t care if it´s a specially hard way like beating a 6 member team against 1 pokemon or something like that, but there should be a way to raise the IVs.
* More previous gen remixes like in ORAS for online gameplay. And being able to use them on Battle postgame content.
* And lastly, as some other user has pointed, let me play gyms with other rules! I love triple battles, but I have to play nearly the entire game with singles...
If all these made into a new Pokemon game, it would be totally awesome. I don´t see most of these happening though...