I haven't read all the responses but I'd get a huge fright if I was in a toilet cubicle and heard a man calling into the women's toilets saying he was about to enter. How do I know he really has a kid with him?
I think I'd be too shocked to respond/protest. So I imagine younger women and teenagers would feel quite uncomfortable too.
I remember having to go to the men's loos with my dad, I thought it was hilarious seeing the weird urinals and yellow urinal cakes. I never saw men using them. If it's a busy enough place with several men using urinals chances are it's a busy enough shopping centre / park and will have its own disabled loo.
I saw a dad take his 2 primary school aged girls into the men's changing rooms at the pools recently. THAT would be traumatic! Especially considering there are 3 family change rooms at that pool.