If you don't have the trip-lever type of drain stopper, it would not need or have the weighted bob stopper. How do you stop up the drain to fill the tub for a bath? It must either have the pop-up/pull up+twist stopper or a rubber stopper unless you use a flat rubber disc drain cover.The missing plate was there when we moved into the house in 1974. It's never been "upgraded" unless done before then which I doubt. The only access to that area behind the tub is by tearing out a wall. Something I'm not going to do.
Never had any smells out of it either.
The P-trap has been required by national plumbing code to prevent sewer gas infiltration way before the '50s.