Yup on the 73 we have the apu running and on both busses before shutting down an engine, with due consideration to taxi route, stand, ramp condition, slope etc etc you get the picture.
However a late change of stand, or as has been mentioned guidance failure, lack of ground staff or a stand you can't self position onto can sc#ew you over a bit.
3 min cool down if using reverse thrust above rev idle, otherwise 1 min.
WBV