While not a specifically approved practice, at our company some may use the MCT detent after takeoff from LAS or RNO or other high altitude or terrain constrained airport on a hot day until the flaps are up and the aircraft is on profile at climb speed.
The FMA is flashing climb but in a 321 the climb rate is so sluggish and the departures are often towards mountains. This is particularly used at night.
The climb power schedule is a customer selected condition. Customers can select the most economical climb schedule as far as engine life and that is the lowest power setting that still gets the job done.
MCT is an FAR part 1 defined limit: 8. Rated Maximum Continuous Power or Thrust (unaugmented) - § 33.7(c)(1)(ii).
a. For each type certificated engine, the applicant must determine the value for the rated maximum continuous power or thrust. The applicant must demonstrate by engine test that the rated maximum continuous power or thrust is achieved without exceeding the operating limitations established in compliance with part 33 and required in § 33.7(c). The ambient conditions for which the engine must produce the rated maximum continuous power or thrust are specified in § 1.1
Airbus Climb schedules could be as high as MCT or considerably lower, as my company's is.