Levelling faster would at least partly defeat the purpose of having a harder difficulty.
I have to agree with this. The difficulty settings should be about allowing players to find the level of difficulty they enjoy best, not about altering improved rewards at higher difficulties.
If you make people feel like they have to compete at the hardest difficulty setting to get the best rewards, the hardest difficulty setting usually ends up getting nerfed in order to meet demands of making it more accessible. That shouldn't be the point of the difficulty settings here.
Yes, with more risks come more rewards, but in this case I think it's ok if the rewards are just a more enjoyable experience from less trivial combat, or a greater satisfaction from beating challenging content.
Some games actually reward you with less at higher difficulties, as part of the measure to make the game more difficult. "Blackguards", for example, awards less Action Points (XP) at harder difficulty settings because having less developed characters makes the content more challenging. "How to Survive" is another game that goes this route, making drops more scarce to make survival harder.