In my mind if the plates don’t turn freely I'd never pull a toad with it because if you made a turn and a plate got stuck in that position when you straighten out the toad could be dragged down the road sidewise. The plates must twist freely.
The only other alternative would be to lock the plates in a straight parallel position and keep the toad’s ignition switch on so its front wheels can turn but I would not recommend that.
Demco KarKaddy dollies use a rack & pinion system (with ample grease jerks) that allows the dolly wheels turn rather than having swivel plates.
Dave