1] There is the commercial reality that air operators will wish to offer services to airfields which lie outside CAS.
2] There is also the commercial reality that the same air operators do not really wish to pay air traffic service providers to provide air traffic services outside regulated airspace (ATSOCA) - hence, they rely on whatever services they can get - e.g. London Military etc.
3] There is little chance of the CAA (Airspace Policy) approving new controlled airspaces except perhaps in fairly rare cases where the movement rate is very high.
4] Those ATC Providers which do offer ATSOCA are likely to collect a quite high percentage of airprox reports as, I believe, was the case with Manchester ACC in the "Pennine Radar" days. Which ATC provider wishes to take on such risks and the associated liability insurance?
5] The "Injun Country" nature of Class G airspace is that there are numerous forms of aviation - (from high speed military to gliders etc) - operating. It is unregulated and a free for all.
Any "safety case" would have to recognise and explicitly state all of the above. However, it would be possible to produce a document which stated how the air operator "manages" his exposure to the above risks. It would have to cover a multitude of points - e.g. aircraft types, airfields involved, methods of navigating, details of any ATS providers with whom the air operator has entered into an agreement for ATSOCA, whether routes to/from the airfields vary dependent on known activity including danger areas and so on.
Even if one did all this, it would not be possible to claim any great level of actual safety was guaranteed since the operations remain subject to the unexpected happening.
If the CAA really wants to build greater safety for these operations then it should be working to build better services for the operators. Someone would have to pay however and, in this day and age, I am sure it will not be Gordon Brown!