The decision as to which company aircraft (flight) is preferred on the the ground first or in any particular order is more appropriately made by the only area that has the overall picture (view) of the airlines operating environment. The Operations Control Centre staff are the only ones in a position to make such a decision. If there is a need to establish a preferred landing sequence then that is communicated to the relevant ATS Centre/TWR as a request and only if it 'fits' the ATS plot.
Operating crews are not in full knowledge of the alternatives available to the Operations Control staff on a network wide basis. Just because a flight is running late may have no impact at all, more likely any impact has been addressed, mitigated or completely overcome by diligent Operations Control staff without crews or more importantly the customers ever being aware of any 'problem'.
This may seem a bit contentious, however, if operating crews concentrated on simply conducting their defined roles (in the cockpit) and desisted from telling everybody else how to do their jobs or run the airline, flight crew blood pressure would return to normal levels and everbody else would be allot happier.
Disco Stu (retired)