I think the point is that at the moment a person must provide a 'primary identity document' being birth/adoption cert, passport, driving licence or residence permit.
But apparently, the police do not check with the DVLA or the passport office whether the individual has changed their name.
This seems utterly bizarre, and bordering on the unbelievable, but I have not seen proof that the police do check, and this and other conversations that people have had with DBS suggest that at the moment this is indeed the case.
Clearly, criminals will exploit loopholes. This seems a particularly simple one to close.
It would be silly not to close it for everything, so we will have to wait and see.
A GRC would be needed to change the birth certificate, it would therefore appear sensible to also check whether the indicidual has been issued with a GRC.
If self ID went through, the GRC would be a massive loophole in this system. As it is, it is a small one compared to passport/driving licence changes.