I was thinking if these things did exist would they be full coverage?
How far could you go with them and would their be areas where they didn't work?
Depends on which frequencies you use. There are some frequencies which allow for long-range communication to happen. That is probably what I think could happen. Ever wonder why police radios always seem to prefer a short range? Of course, there could be areas where it might not work - remember, even the TV networks don't have full coverage of the entire country - but that would be minor, since anything involving radio frequencies would have those problems. To avoid that, I could probably think of placing antennae on top of mountains and on top of tall buildings.
What good would they do then? You'd still have to use a payphone.
What about those areas that don't have payphones, let alone telephone service?