Rape kits don't necessarily show consent or lack thereof, which is crucial but usually ends up boiling down to being a he-said-she-said problem. You could know who the rapist is with a rape kit that also points to the same person and still be dragged through the mud with the "you must have enjoyed it because you're a slut/you slept with him/her in the past" kind of crap - not many people can deal with that so.....yeah. Plus they are not always the end-all to a rape case even if you have proof of physical contact with no consent.

That's before you even get to any problems before you reach the rape kit stage - I've read way too many depressing posts on r/twoxchromosomes and other sites where women don't even know if they've been raped because they don't remember it after being drugged (good luck with a kit that late) or don't think it "crosses the line" or are just like "it was a bad night" if their boyfriend rips their clothing off and tries to have sex with them even though they were saying "no" and crying the whole time. Usually comes hand in hand with a culture that likes to perpetuate bullshit like "you can't change your mind in the middle of having sex" and "married people can't be raped by their partner".

Gooood luck with rape reporting in general, there's a reason - no, many reasons - why so many people keep silent.