There are different ways of making a Pokémon hard mode.
higher level opponents, more Pokémon on the opposing team, less exp gained, and more (think of how Hard modes are traditionally designed in other RPGs and apply that to Pokémon).
To this, I would say no, because for me it wouldn't be genuine and fair difficulty, it would just add a lot of grinding.
My "ideal" Hard mode I'd love to play would be something like this:
-Trainers with smarter teams and movesets, and better AI (keeping it balanced and reasonable of course, no dumb stuff like giving the first/second gym leader a full six team, moves that are OP for the early game, or fully evolved mons right away)
-Give important trainers held items to further improve their strategies and make players improve theirs.
-Gradually give trainers more EVs as you progress through the game so the player's team doesn't get a major stat advantage. And give important late game trainers good EV spreads.
-Disable the free switch on KO option, and the use of items during battles that can completely trivialize the intended difficulty. Players who want more challenge normally don't use these features anyway.
-Add level caps (another aspect many players manually handle themselves). If a player needs to overlevel to overcome a challenge, then that player didn't actually learn anything from it, and either the player or the game is doing something wrong.
So imo Pokémon games should try being less about levels, and more about strategy, thoughtful team building, and proper understanding and use of the tools you have, so that good team work and doing your best with what you have is the key to succeed. When I play modern Pokémon games I'm sometimes more worried about which trainers should I battle and which should I skip to avoid overlevelling than actually having fun, which is just pathetic. I don't want that, but I also don't want the opposite of having to grind levels because the game has suddenly absurd level spikes. So easy level gain but addin level caps seems like the best solution.