Obviously it's a known practice, as you know about it.
There are no "rules" saying a pilot can't do so, if they consider that a safe course of action. There are a couple of types of emergency call for a reason, though -
Call "MAYDAY" when you have a problem, need priority in the air (and/or navigation assistance) AND you suspect an unsafe emergency landing could result - this helps the ARFF commander to decide if they need to decalre a full emergency response (i.e. notify hospitals, ambulance services etc etc)
Call "PAN" when you have a problem, need priority in the air (and/or navigation assistance) BUT once, you are at the airport you expect a safe landing to be made (e.g. - a medical incident on board etc)
It would be quite normal to decalre a MADAY for an engine fire, and downgrade to a PAN once you are sure the fire is out.
In any case, the airport emergency response will be decided by the ARFF commander - they would probably stay on local emergency standby for the landing even if the pilot had "cancelled the emergency".