why is he gaining experience? Once he's above rank F he can't steal skills anymore without a penalty right? He should just be History's Strongest Rank F. There's quite a few stories like that!
The downside is reliving the worst trauma of whatever killed him, either the worst thing they did or happened to them. At F there is no downside, at E he witnesses the trauma and higher ranks he feels the pain ect. Basically he is tortured in a personal hell for a little while before he wakes up 24hrs earlier.
As for why he gains experience
He is limited to 4 skills at a time currently, but he can trade 1 skill for another if he wants. At higher ranks he gets stronger, and can have more than 4 skills.
@firosahoge there is a limit to how many skills he can have. At rank F he can have only 4 skills, he can exchange them but because his first 3 skills are op he can only change 4th one. When his rank increases his limit also increases so that's why he is trying to level up.