I have no idea why nosewheel steering is not fitted to both sides on all aircraft but here are two interesting points:
A, Debonair had a fleet of BAe146 with steering on both sides. We then bought three aircraft from Air Atlantic in Canada. All three did not have nosewheel steering on the right side. Caused a bit of confusion with two sets of proceedure for F/O take offs.
B, Crossair have all Avro RJs with right hand nosewheel steering but they prohibit F/O from doing any take offs.
Funny is it not?