They used to do that...at least in New York State. I worked as a C.O. and Sergeant for 25 years. As a rookie C.O., I ran the phone program at Auburn Prison (max). It ran on the 3-11 shift. They had five or six phone booths in the basement of the admin building, and inmates got two calls a month that they had to pre-schedule, in order to make them. The inmate would be checked off the list at the gate before being allowed to come to the admin building, and I would make the calls from a list of the approved numbers they could contact. I'd get the operator to connect the call, and ask the other party if they'd except charges, then once that was completed, the inmate would go to the phone booth, and had 10 minutes to talk.
Today it's all different. At the max prisons, there's phone booths in the yard that they can use when the yard is open. I retired from a medium prison in 2003, so I've been out of the loop for a long time. There are probably more phones available at other places in all the prisons. The prison I was working at had phones on the housing units they could use after a certain time, and phones in the yard. The calls were all still monitored and recorded.
Yeah that was a long time ago. Figured it was all different now. Gotta make everything easy for them.