One system I have seen that tends to help is the establishment of a number of "corridors". For example, it is usually a safe bet that one can transit the Brize CTR through the overhead (well 1nm East or West) at 2000ft QFE or 8nm East or West not above 1500ft. Maybe this type of system could be explored to reduce R/T? I reiterate that stating time before crossing on initial contact may have some merits. At least this may assist the controller in assessing his priorities.
Nevertheless, we have to remember that for a controller to identify an aircraft (almost a necessity to guarantee a CTR transit nowadays), apply a service, allocate a route, issue a clearance and get an accurate readback all takes time, something that is often lacking.
Finally, I am not sure about the efficacy of giving an ac an indication of the possibility of transit on initial contact. With some of us, that may well lead to more infringements as we would blindly head off towards the boundary only to confirm the status of the (non) clearance on crossing the line.