Fun fact: 56 kbit/s even as a theoretical maximum never existed in the US for dialup. FCC regulations on transmitting power over POTS limited it to 53.3 kbit/s.
Even that required very good operating conditions. The phone network was rarely that good, because it didn't have to be. You needed to have good copper all the way to the ISP (by no means guaranteed), a good connection at the CPE (which wasn't always a given), good wiring (very rarely a given), etc. There also only had to be one ADC in the path (which was not guaranteed although usually the case).
Modems would actually negotiate the data rate by checking the line quality. It would vary each time you dialled in. The number you dialled also had a major impact because it depended on where the other end was located. Sometimes in busy areas, you had to try different numbers to get the best speed.

