In my experience as a controller I would say that neither myself nor the controllers at the diversion airfield are interested in a reason for a non emergency diversion. Indeed when this occurs, most pilots will state that it is for "operational reasons",and that is all the info that ATC need-you want to divert,it is otherwise ops normal. Although if an airport is pushed for parking space,they may only accept diversions for emergency,in order to keep their own operation moving.
When I do have to ask a pilot for a reason,the request has usually come from the airport ops people. I guess they need to know what facilities you need to use,how long you will be there for,whether they have enough space to park you etc etc.