Airlines have to consider things like:-
. Are GPU's available dowroute
. Are airstarts available downroute
If the answer is yes to these then there is not really a problem with flying without the APU. the only real problem is that it can sometimes increase T/R times due to having to start up before pushback and conecting GPU's etc. for example easyjet allow and extra 10 min if the A/C requires an Airstart. Hope this answers your question
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brgds BB