If you drive with an expired MOT or less than minimum tyre tread (illegal of course and subject to a small administrative penalty) it does not totally void your third party liability cover.
This AIUI was done on public policy grounds because many drivers drive without an MOT, a license, road tax, or some combination, or an unroadworthy car, overloaded, blind drunk, etc, and if this voided their insurance, the mandatory insurance requirement would be close to worthless.
And 3rd party motor insurance really is badly needed because 3rd party damage is very common.
I don't see anybody caring much about public policy in GA, which is why the insurers are not forced to maintain the 3rd party cover even on totally illegal flights, but given the 3rd party risk is negligible, why was insurance made mandatory in the first place??