Yes, a common misconception. Section 143 refers to use / users and not to keep / keeping - which, in law, equate to use by driving or moving under power and to leaving standing or moving not under power (with certain exceptions.
I entirely agree with you that there are risks attached to 'keeping' and certainly to certain acts of pushing, towing or storing inflammable fluids etc. However, these are not against the law.
You may be interested to know that the RSA of 2006 stopped this gap because of risk to others in public places or on the road in such places as car parks following a case that is hilarious to read except for the fact that in the claims involved people were badly hurt. See - House of Lords - Judgment - Clark (A.P.) and Others v. Kato, Smith and General Accident Fire & Life Assurance Corporation PLC Cutter v. Eagle Star Insurance ...
The RSA amended the RTA to add keeping to Section 143 . . . only it has not yet taken effect.
The MIB was no such thing . . . it is not only drivers but anyone else affected by the uninsured use of a motor vehicle.
So there you are.
Regards Funforus