I don't honestly think Pokemon needs a difficulty adjustment - fans are quite capable of setting up their own difficulty modes with challenge runs and the like. If you want to make Pokemon harder, do it yourself, because the devs won't do it properly for you, I can guarantee that.
The problem is that most people equate difficulty to how time consuming something is, which is a painfully false impression. Once you've levelled up you will still curbstomp your opponent. If you can grind your way out of a block, then the block isn't really there - it's just designed to make you play for longer and make you think it's harder than it actually is. If it's not that, then enemies just hit harder, you hit for less damage, and HP is ridiculously bloated. That's not increased difficulty either - that just means you have to grind longer or take longer chipping away at a ridiculously large health pool whilst the enemy pounds you with the same moves. The only thing challenged is your patience.
But if it were me designing a hard mode that was actually challenging, I'd do a few things:
1. Make the AI significantly more intelligent. Challenge Mode in B2W2 was a good start by giving opponent Pokemon held items and increasing their levels, but I don't think the level increase is necessary with my second point. What would be better would be if the AI fought like a human opponent. Randomise attack patterns. Make Pokemon movesets balanced and threatening. Make use of status effects. Switch out when in trouble. Do all the things you might expect a living person to do, not just a braindead AI.
2. Cap levels. The problem with Pokemon is that you can grind your way through anything. Put a stop to that - have it so that you CAN'T level past a set point until you get that Gym Badge...and have a Gym Leader's Pokemon at that level, so you're evenly matched. You can still have a type advantage, but that's just playing the game strategically, and if an enemy has moves that make up for type weaknesses, it's a fair game. You have to think about what you're going to do. Exploit all your advantages, rather than just grind until you can one-shot everything.
3. Restrict item usage and number of Pokemon you can use. Make it two-on-two, or three-on-three, or whatever, with a limited inventory. Make it fair.
4. Provide options. A few hacks have Nuzlocke settings, and some of the best RPGs will let you adjust gameplay settings for your own experience. Draconian Mode in DQXI lets you handicap yourself quite severely. Bravely Default let you set your own encounter rate, which was amazing. No matter how hard you make a game, someone else will find it easy. So let the player decide how difficult they want to make the game - just give them the tools to do so. For Pokemon, you could lock levels, have them permanently confused, loafing around every other turn, neutralise abilities and hold items...the list goes on and on.
As for Easy mode...well, the games are already pretty easy, but some things I could think to add would include OHKO mode, Invincibility, EXP multipliers, guaranteed catching regardless of Pokemon HP, and so on. The Final Fantasy remasters/ports on current generation consoles have some absolutely fantastic mods; a system like that which you could turn off and on as you please could make the game even easier, and give you the chance to experience something more challenging if you got bored with that.