I am not suggesting profitable ways of modding games, even less suggesting itch.io to have specific mechanisms in place to help moddable games profit (eg.: steam marketplace). I think it is up to the game developers to make this choice and balance out if it's worth it or not.
The specific case where I though about this being a possible feature was when playing a small broken free game (which I could say amount for most of itch's library), that I felt compelled to "fix", and though itch could have interesting ways of incentivizing that behaviour, instead of me having to DM the game's author. It's a very tough conversation to have, and I think with certain incentives, itch can "educate" people to even start thinking of the possibility of opening up their free broken games they expect nothing with. Would be almost like promoting a game specific "licensing" idea and helping users out with it, by say, asking some additional questions about how you think your game can be modded/shared. (kind of like the CC questionaire you answer to know the best CC license to choose for your assets)