If I understand you correctly, Q, if you re-install the ignition switch back onto the lock cylinder, the steering wheel locks when the car is started/key is in...
BUT, if you keep the ignition switch dangling, everything's OK?
If that's the case, my only thought is that this may be some type of redundant security component.
I did not replace my ignition switch back onto the cylinder - no point, really, since mine is frozen. There should be enough space under the dash to stash the ignition switch. If not, remove the lower part of the dash and gently place it somewhere inside there. It's not full of space, but there should definitely be room.
With my ignition switch and A LOT of extra wiring (I went overboard with the length of my wire), I was still able to store everything underneath the steering column and reattach everything to make it look normal.
If you're still having trouble, take a pic and I'll see if I can help further.