Per-call billing sounds crazy - there should never have been a time in circuit switched or packet switched networks when that would have correctly captured costs.
I don't know about the OP's situation, but at one time most phone calls were completed by a human operator looking up circuit numbers and physically connecting the two customers using a patch cord.
I suspect that under that model, the operator's time was the dominant cost involved in placing the call.
1) The customer paid a fixed monthly charge for having phone service at all. This covered the capital costs of the wiring to the customer's premises.
2) On top of that, the customer paid a per-call fee. This covered the cost of having a woman (usually) ask what number you wanted, locate the proper jack, and physically plug your circuit in to the circuit of the person you wanted to reach.
It's probably no coincidence that the local service operator was one of the first parts of the phone system to be automated away (nor is it surprising that phone companies continued the per-call charge long after its justification went away :-)).