Correct my "wrong-headed" beliefs if you can, but I suspect the sexually desperate are more likely to rape. This column presents evidence that sex crimes go down when the internet is introduced.

Right, this evidence is one of the strong pieces of evidence that undermines the entire rape-is-about-power claim. And there's other evidence for this also (for example, prison systems that allow conjugal visits have lower rape rates than those that don't(a citation for this claim would be nice. I've seen it before but a quick Google search doesn't turn up anything useful)). But sometimes, it is about power. Indeed, the type of rape being discussed in this context, by someone like Draco is the classic power situation. And when people are raping enemies that's more or less unambiguously about power.

Wikipedia on motivations for rape

I think it's complicated. Even the access to the internet lowering the incidence of rape could be about increased chances of finding partners as well as access to more porn-- it isn't as though porn was rare before the internet.

My impression is that it isn't as true as it used to be that fictional evil characters are ugly, but I don't have stats. It's certainly reassuring to think that the people you find repulsive are also more dangerous.

Interestingly, I actually had a specific female Death Eater that I had in mind when I wrote that post. The character in question, Bellatrix Lestrange, was played by Helena Bonham Carter, who does not strike me as unusually physically unattractive.

Ceteris paribus, girls are far, far less desperate than guys. Supply and demand says an egg produced once a month will have a higher asking price than what guys churn out. This makes me suspect female rapists must be less attractive.

There may be different factors going on for female rapists. The statistics you cite don't separate out male and female rapists, and I suspect that female rapists are less likely to rape out of desperation, rather than being less attractive.