"Surely the harm posed to grown women by a man taking his small daughter into a ladies loo is much less likely than the potential harm posed to a small girl who wanders alone into a mens toilet (thinking it's OK as she's been in there lots of time before with Daddy?)"
Have just taken a few minutes off sitting around in a public lavatory to prey on women and children (it's what we all do in there, don't come in, ladies!) in order to answer this.
The only thing I have EVER been aware of men doing in a public toilet is pissing and shitting. Presumably, over the years, I have been unwittingly present while some hot consensual gay action went on behind a locked cubicle door, ditto graffiti writing, perhaps even cigarette smoking.
Is it different in women's loos? Is it full of paedos on the prowl? If so, I fully understand your fears.
If not, I do not think you have a very strong grasp on what "risk" is.
Even accepting that there is a risk of harm to a child in a men's toilet - and, obviously, I frequented these places very young and have never, EVER been approached by anyone - there is no reason why any sane child would think it was all right to go in there without her dad just because she had gone in there with her dad; unless, as I say, you think that because a child has crossed a road with her dad she will think it is okay to do so without him. How do we prevent this possibility? We say, "don't do it." And, without sensationalising or scaremongering, we tell them why.