I'm assuming one of those "benefits" is making women feel uncomfortable in women's bathrooms?
If my wife or 7 year old daughter went to a womens toilet and some bloke went in there got his cock out in front of them and claimed he was a women, then he is putting himself in line for a beating, if he had just gone to the mans toilet in the first place that situation wouldn't arise.
The op you both quoted clearly stated they are in favor of separating them by genitalia, rather than by "Men" and "Women". The scenarios you both used wouldn't happen if they were separated by genitalia.