Games are usually optimized for normal difficulty.Most devs have sloppy hard modes. It's more difficult, but not in a good way, so I play on normal. Put differently, the devs intended the game to be played on normal. The hard mode is just a generic "add more enemies, health, decrease drop rates" but the thing is the levels are made for normal in mind, so the game won't be optimized well for these types of hard modes.
I like it better when games only have one mode, but there is enough depth to make your own hardmode. For example whip only in Castlevania games or 3 heart runs in Zelda. These rather creative ways to increase the difficulty are much more interesting.
Then there is the question of achievements. "Complete this level under x mins" these are fine, but only if the level design is time attack-friendly and the controls must be tight and reliable. So for example trying to speed run a shooter with constant gameplay halts is not very giving, but completing the time challenges in Meat Boy is highly intense and satisfying.
tldr: it depends.
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