Unfortunately, I have to agree that Coventry are becoming over protective of "their" aircraft when it comes to transit traffic. It isn't uncommon for them to "control" passing VFR aircraft in Class G, in some cases to give 5nms separation.
This will result in some pilots choosing not to talk to them at all, as they are at liberty to do, which is counterproductive.
It is worth looking at the proposed large chunk of regulated airspace Coventry are demanding. The airspace they now wish to control is a main VFR and IFR GA transit route, if not THE main transit route of central UK. The proposal, if approved, will effectively close the gap between Brum and East Midlands airspaces and will cause a choke point to the east of Coventry where pilots aircraft cannot make MSA (1700 feet) but will be tempted to go under the CTA (below 1500 feet) to avoid delays.