On the one occasion I had to make a Mayday (minor mid-air collision, if there is such a thing) I called both on 121.5 and local airfield frequency, as I thought it likely they would be interested and possibly even have to take any necessary action.
I didn't start the call with an airfield full identity, only position of the incident, since I was mildly busy at the time enduring the sircraft was sufficiently controllable and stucturally sound enough so that I didn't need to rely on Mr Irvin's useful product.
If any controller had complained I would not have bothered to respond until later, when I might have considered an appropriate discussion.