Ok yeah, considering that most people would prefer not to commit heinous acts of violence (without good reason, that is) + we glorify violence in the media, it may seem as if there's no correlation between type and an aversion to blood/violence/gore, but there is.

The difference between EIIs and other types is that the discomfort lingers. Context matters too. My mom and brother (EII) can watch Game of Thrones because they understand that it's not real + it serves a (fictional) purpose, but it hits a much deeper place, and they may not even realize how deep it hits them until they stop exposing themselves to those things and realize how much happier they are for it, hence: "...for every event, even those popularly deemed insignificant, leaves a trace in her soul that survives for a long time." among other Si HA/Se PoLR excerpts from the descriptions.

It's the aftermath, not the simple act of avoidance, that separates EIIs from other types. IEEs are similar. So it's not as if the alternative is SLEs reveling in it. It's that it may make them uncomfortable in the moment so they'd prefer not to expose themselves to it, but it won't stick with them for weeks/months, and, if it does, then it's probably not an SLE? Otherwise you're reworking the whole system to fit something that just doesn't fit.