I civvy street, an annual airtest is carried out for the authorities. This is to alert them of any degrading trends. I have often been asked by the Authority to have an aircraft re-weighed due to a downward trend in performance.
Airtesting the aircraft after an engine change is done for the same reason. A simple timed climb to hight will show if the engine is producing the real goods. Even if the engine has been brake tested, disturbing its 'arteries' and controls can often give rise to a lack of power or other problems. Dirt in the system etc. I airtested an aircraft once that had an engine change and a generator had been fitted with the studs in the wrong wholes. On any other aircraft it might have been ok but this one had a problem with the throttle linkage which for some reason only became apparent in flight and prevented the application of max power.
Lastly, Air testing is always a good idea after any major operation, so to speak, it means an experienced guy gets the first go and is expecting that something might go wrong. To suddenly 'present' an aircraft to a line pilot after major work, the risk is almost certainly greater. That's why the Authotities have pilots approved for air testing! It just makes good sense.