<<I just think it would allow ATC and pilots greater flexibility to get into and out of central London.>>
Most of the helicopter routes cause no problem at all. It's those close in to Heathrow which may do so.
Access to central London by helicopters has little to do with the airspace classification but has more to do with single-engined aircraft flying over built up areas. Twin-engined helicopters can be routed on direct tracks away from the heli lanes and, so far as I know, there are no restrictions on single-engined helicopters using the heli routes as a result of the Class A classification. Equally, twin-engined light aircraft can also fly SVFR over London and anywhere else in the zone as long as they do not conflict with Heathrow, Northolt and London City traffic.