The "one phone call" is a myth made up by Hollywood. Last time I was arrested, there were several phones in the holding cell, and I was there for four hours. I could make as many phone calls as I wanted, to anyone, either local or collect.
I don't think it was a myth so much back in the day - the supreme courts ruled that if you were arrested, you have a right to contact someone. I.e., the police could not arrest you, then toss you in jail without you being able to talk to someone who can try to do something about it.
Perhaps it's more apt to the smaller communities, you know, the ones where the cops are just as crooked and looking to arrest you for any reason whatsoever. The one phone call came into play saying you were at least to have the right to contact someone - otherwise the police would just lock you up for a month, then set you free.
In most "normal" areas, yes, the phone is freely available for use because the last thing anyone wants is for you to be let go because you did not have sufficient time to contact someone, especially an attorney.
So today it's more likely a myth, but back maybe 50 years ago, it probably wasn't. Plus probably a bunch of court precedent that basically said under what conditions that "one call" really meant (is it one call, and if you reach a busy signal, no answer or an answering machine and that's it?). Just safer to let them have use of the phone as much as possible so no lawyer can get the guy off because he was denied sufficient phone access.