Just to add my two pennyworth to the debate, without sounding sexist, might I suggest that the main use of public toilets is men wanting a pee (often after drinking far too much of the falling over water). Unfortunately the enclosed nature of lavatories makes them prime targets for vandalism, drug taking and all sorts of unsavoury activities.
(I seem to remember a sketch with Spike Milligan as a lavatory attendant who came out with he memorable phrase that so many strange things went on in his lavatory that someone coming in for a shit was like a breath of fresh air).
The continentals have had their pissoirs for years and as can be seen from the attached photo London are now bringing in high-tech ones.
Perhaps the introduction of a few of these at prime sites might be the way forward?