Long story short, my Prisoners' Family need is very high. I have built a phone booth room, but no Prisoners are using it!
Here is a quote from the PA Wiki:
Prisoners will use phone booths during Free Time regardless of what room they're in, so long as the room is not marked Staff Only in the Deployment screen.
There is plenty of Free Time on my Regime, and the Prisoners are all active (elsewhere) during it. Neither the room nor the area around it is Staff Only etc.
Why are Prisoners not using the Phone Booths?