Why not courts? Courts are constitutionally required to have a higher standard of evidence than other institutions. In the usual case where a rape has absolutely occurred, the evidence often amounts to he-said/she-said. That's rarely enough for a conviction. That's understandably deeply dispiriting to anti-rape activists, so they move activism toward places that can afford lower evidentiary standards.
Is that the right way? Who knows. But I think it may be best to treat sexual assault as an epidemiological problem. That's hard to swallow--after all, rapists are bad people and deserve severe punishment, not dry statistical treatments. But given how hard it is to "fairly" prosecute rape, treating programs to end sexual assault as interventions to decrease incidence and then measuring how effective they are seems like it may be more productive in the long term.