Things I hope for:
1. Difficulty Option - I want my battles to be more than hitting something 1-3 times so that it faints. Pokemon have always been too weak, including unfortunately, Legendaries.
Type advantage would need a huge rebalance as it's far too overpowered. Ever since I was a kid I played a "single mon per gym" style, for example. This means that as long as you have a type advantage on that gym, you can beat it entirely using only that single Pokemon. I used to play this way to catch up stragglers on my team in levels. "Hm, my fire type is lagging behind, I'll let him solo the entire Ice gym".
Trainers/Gym Leaders/Elite Four should always have access to items just like you. The fact that even the "highest ranking" trainers use, at best, two items just makes them seem absolutely incompetent. You always have access to an abundance of potions, stat boosts, etc, yet the trainers in that same level range do not? Makes no sense.
Elite Four members need to no longer use same-type teams. This goes in line with the type advantage's critical flaw and making "powerful" opponents look like they're fresh out of their hometowns. Any competent trainer is using a mixed team, not a single-type one. Training wheels should be taken off for the highest level of competition.
Items against the Elite Four/Champion will also be restricted. You may only use what you're provided. Example: 5 Revives, 20 Super Potions, etc is all you get for the entire thing. This puts more emphasis on building proper teams and less item dependency.
Better enemy AI, including wild encounters. Pokemon are more likely to combo attacks, avoid using less effective moves unless they have to, etc. Trainers will switch out if a better option is available to them, just like the player is often going to switch out their Grass-type when the opponent has a Fire-type.
2. More fleshed out game content - I'm honestly tired of the bad post-game Pokemon games have. I don't want any more luxury resorts as a reward for beating the Elite Four. The Elite Four shouldn't even be as low level as they are. The last 40-50 levels in Pokemon seem wasted every single time. Either structure the game so the Elite Four are upwards of Lv80-100, or actually provide challenging, rewarding (exp and so on) content after you beat them. Though, the best idea is to just make the Elite the absolute end-goal, since it honestly doesn't make much sense that there are so many trainers in these resort areas, because that implies they're all champion-level. I doubt that.
Make it so the game isn't just about going from gym to gym. There should be more along your journey than just gym towns, that way you progress enough and see so many different Pokemon before finally reaching the Elite. You can have "side quests" be part of the main experience. Instead of the next thing on your list being "the next gym", it could be helping this group of scientists with their research, which leads you to __ Island, and you encounter all sorts of things there. After everything you go through there you eventually return to land and progress to other towns, which still don't have to be gym towns.
I want the game's progression to feel more organic, and like a huge epic adventure rather than just going on a gym-tour. I think the adventure aspects feel better in the anime from what I remember, as an example. More things happen along the way to the gyms and whatnot than the games offer.
3. Fewer Mega Evolutions - This is a neat concept, but it honestly feels more like padding than proper content, especially since some of them are still quite bad and anticlimactic because of it. It's also wasted on Pokemon that were already great to begin with, while the many Pokemon that could actually use a boost get nothing whatsoever.
4. Day/Night cycle like GSC - This isn't huge but it'd be a nice return, and fitting with the "Sun and Moon" theme.
5. Tone down HM dependency - Wasted slot in your team, or wasted slot in a Pokemon's moveset. Abilities like those should be inherent ones in Pokemon anyway. A Water Pokemon should always be able to "use Surf" in the field without needing to know a specific skill, for example. Could even get creative with that and have flying/levitating Pokemon be capable of taking you over water as well; burning down shrubs instead of needing Cut. This way at the very least you have more options to get through things instead of needing one specific skill/Pokemon as much.
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Overall though, I just want a whole new place with a brand new attitude. A place where I feel like I kind of still have to catch them all and be the best that I can be.