As for the H&E, it would mean that CG helos would not be able to operate in weather conditions, which would be allowable in the RAF. However, i do realize that the CG are introducing All weather Helos, but they are still not in full supply.
In addition, At one time, all SAR was provided by the RAF and so the Defence budget had to include provision for them. However, if the Coast guard were to take over the main SAR provision, then the bean counters could say that they could include providing SAR cover for the forces, thus eliminating the need to keep both helos and trained crews in the RAF and Royal Navy, who could transfer to the CG. That would also mean cutbacks in the support services such as the Rescue Centre at Kinloss. So the Defence budget could be pared back even more