Quote from PDR1:
"Shore Power" is fine where the services required are electrically driven. Cabin conditioning usually isn't. There's also the detail that it would need to be metered and billed, which just adds more administrative bumph which would be difficult to justify when the aeroplanes all have perfectly good APUs."
I retired many years ago, and am not au-fait with curremt regulations at airports. However, during the 1990s the major European airports gradually introduced swingeing restrictions on the running of APUs, due to local noise and air pollution regulations.
On arrival it became the norm to shut down the APU as soon as ground-electrics had been established. At some airports the APU was not even started, which meant that one engine had to be left running instead. That would be costly on occasions when the dispatcher (or other competent ground crew) was late arriving at the gate. In extremes of ambient temperature, "ground [air] conditioning" would be supplied (eventually) for pax comfort during disembarkation.
A similar logic was, and presumably is, applied for departure. The APU was started only a few minutes before departure, to facilitate engine start during push-back.
I'd be very surprised if these airport restrictions on APU running have been lifted since I retired. More likely, they've been increased! From a pilot's point of view, the only redeeming aspect is that, if the APU is u/s, the ground services are more likely to be geared up to greet you on arrival.