Been thinking about this for a while, and don't see why it shouldn't work.
TV Licence Detector vans are given a list of addresses which do not have Licences, and just go and check them out. The DVLA have a list of all registered cars, and there is a database of Insured cars. All that needs to happen is for the Police to attend those who have a registered car with no entry on the MID, and ask to be shown the car.
To me, this would be the obvious way of getting rid of uninsured cars, if this was the genuine intention. The fact they use unmarked cars to catch the odd one or two does not show a determined effort at clearing the roads, just a way of collecting income.
A further thought on this is that a whole new Department could come into being, enabling Govt to employ another few thousand thus reducing the unemployment register.