This is what Airbus says:
It [Maximum Continuous Thrust] is the maximum thrust certified for continuous use. This rating should be used, at the pilot’s
discretion, only when required to ensure safe flight (engine failure).
If you take the case of A321, you will find it's very sluggish to climb when it's fully loaded. I have seen Captains using MCT to overcome this.
Sluggish as in what? Low rate of climb? Fully loaded commercial aircraft doesn't have the performance of an F-18 and most of the times you just have to accept it. Tell the ATC "unable" and drink your coffee...