So far we have all focused on the needs of both parties to get their respective jobs done, in the case of a go-around.
I wonder if you will all allow me to propose a possible solution, as I feel that discussing solutions is useful.....
The pilot(s) know why they are initiating a go-around, so why not just report that in the same report of ".....going around due xxx."
A lot of ATC units have instant playback of RTF calls, so the ATCO would be able to listen to the call again and again, if he/she missed it and would save asking the pilots. Then when the pilot(s) has the aircraft under control and cockpit workload permits, a dialogue for a solution can be discussed between ATCO and pilot.
This is just my 2ps worth........please feel free to comment or add your own possible solutions!!