At my airfield ALL engine tests are to be approved by the tower as well, whether idle, low or high power. The times of these are logged by ATC. I believe this is more due to potential noise complaints. For high power runs the aircraft will be positioned to a remoter part of the airfield. If we get a noise complaint, we can check in the book whether it was a low or high power one at the time.
Also, we will be aware that there is an aircraft with the engine running and can provide cautions to others if necessary, or if something goes wrong alert the fire service and know which aircraft, where, and how many POB.