I spoke to Egg, and they do appear to have thought about it a little after all.
The primary account holder has to sign up to their blame-shifting scheme first, and apparently the secondary account holder can then set up another password. I say “apparently” because this has yet to be tested. In this case the secondary account holder signed up first. In order for the primary account holder (me) to sign up first, the secondary account holder (Wen) has to first de-register, and then re-register after the primary account holder has registered.
If this works, I might then try de-registering myself and see if I can continue to get away with not signing up to their evil one-sided conditions, leaving Wen to wallow alone in implied fraudulent complicity should anyone at the bank steal anything.
And to put a ribbon on it, my NatWest Maestro cashcard is now a Visa debit card, and is afflicted by Verified by Visa as well.