You need two things to get an aircraft to start. Electricity and an air supply. Normally the APU will provide them, but either or both can be provided externally. Once the engines are running, on a 747 the APU is nothing but a dead weight until it arrives at the next destination. It cannot be started in flight.
When we arrive at a port, the APU is started as we approach the gate. The air load is transferred by turning on the APU bleed, just prior to engine shutdown. The generators take over the load as the engine driven ones drop off line.
As you had to wait for external electricity, you either had a totally unserviceable APU, or you had one which could provide air, but not electricity. An APU being either totally, or partially, unserviceable is not a big issue, though it adds a few minutes to both departure and arrival procedures.
No APU, or one that cannot provide air, is a real PITA in hot conditions, as if forces us to rely on external air conditioning, which is never as good as the aircraft packs.