The solution goes back to communism.
I lived in Brno and Trnava (Czechoslovkia) shortly after the fall of communism. I won't say public toilets were always assessible, but if you knew your city geography, you could arrange your walking to be within 20 minutes of a facility that you could use.
These facilities were managed by a couple of people, probably 50+. Easy work, kind of what these people needed in their later working years.
I heard that having the people there was useful in preventing vandalism. Maybe a real study would be useful.
The fee was 5 crowns, but if you complained that you didn't have the coins, they let you through. With the 5 crowns, you got a little wad of toilet paper. Most of us carried some extra in a back pocket or purse.
The facilities were fairly clean, perhaps a bit short of my standards. But better a little dirty than not being there at all. I heard some real horror stories of facilities in Russia.
In your original article, the photo of the one-stall public facility in London might be shiny and new, but it seems like a step backwards from what the communists had created. A small building with four stalls for both men and women. No lineups.
I haven't been back to Trnava since 2003. Not sure of the state of public facilities any more.