Insurers already work with the police to maintain a database linked to the PNC system which police can access which indicates if a car might be uninsured.
Problem is that in this country it is a given right that we are not obliged to carry any driving documents with us. Technically if a police officer asks a driver to show his licence, the failure to provide is an offence, but the 7 day wonder process is the legal get out.
Blame the civil liberties bods who would object very strongly to us carrying any driving documents, licence, insurance, etc, just like they object to anyone having to carry the Identity cards if they come in (which IMO would make those pointless - but that's
). Changing that arrangement would be a major change in UK law, one that is most unlikely.