My steering wheel doesn't lock. No sway, and yes I have a turning table on the dolly. Many modern cars no longer have a locking steering wheel.
The rationale for unlocking it is the turns put a lot of stress on the steering mechanism and the only thing locking the front is a small pin usually in the transmission. On the other hand, towing unlocked some say you can get excessive sway.
The pin in the transmission is for "P" park. Nothing to do with the steering. You remember the warning of laying into the tranny when in park. (like on a hill). The pin in the steering column on vehicles so equipped is quite stout.
While we're on the subject, saw a class A gasser today with an Envoy (or it's counter brand equivalent) on a dolly, rear end up. That was fun to watch. Now the toe in is working AGAINST you. THAT was sway.... a lot. Enough to jerk the hitch around which has an 8 foot arm to the rear axle.
Dude is probably blaming his shocks for the fact that he can't keep it on the road....