I'd say 99.99% of women, girls even, have received unwanted sexual attention - whether that is leering, cat-calling, sexual threats, touching or worse - in public places, schools, going about their every day lives, most of them before they've even hit their mid-teens and it doesn't let up until you are deemed to be 'past it', at which point you become either invisible or the butt end of MIL jokes, old biddy comments and the like. So when we say we'd rather not take a chance that men will behave in confined and intimate spaces like changing rooms, our cynicism comes from our experience of trying to go about our ordinary lives in peace.
Perhaps we should take health and safety legislation as a good parallel. Most organisations are well run and take their duty of care to their employees well. Most people are sensible and would prefer not to loose a limb at work or have a live-changing injury. However, there are some workplaces which are innately hazardous because of the nature of the work, whether that is a sheet metal plant, a chemistry lab or a construction site. Do we say, "hey, don't worry - everyone is sensible and employers can be trusted. Let's not bother with safety guards around cutting tools, or fume cupboards or protective clothing, or guard rails along scaffolding. Everything is a-OK"? No, we know that some situations are more likely to give rise to accidents, that people occasionally have a lapse of concentration, that lots of minute exposures - whilst being unlikely to cause immediate harm - could lead to a preventable occupational disease like asbestosis. So we design our workplaces to mitigate risk, to minimise preventable harm. People grumble and roll their eyes about "elf 'n' safety gorn mad", but a lot of accidents and occupational illness is prevented day to day and over the course of a year, a decade, a generation.
Same goes for women's/sex-segregated changing facilities, toilets, prisons and hospital wards - they mitigate risks, minimise preventable harm, significantly reduce assaults. And that's before you even get on to respecting women's dignity and privacy to deal with biological issues like menstruation that men do not have to content with.
Anyway, I sense this thread is great sport for you given your wilful misinterpretation and mansplaining...