It would still be far more to the point for the pilot to telephone the watch manager after parking. That is not what the RT is for and can really spoil the ATCO's concentration in what was obviously a busy situation.
I don't know quite what point the pilot is trying to make. He made the decision to fly a missed approach - that's his choice. He should be bl%dy grateful that it doesn't happen every day at somewhere such as LGW where, really, it is a national disgrace that so many movements are planned on a single runway.