My two cents, but only based on thinking about and not based on real knowledge.
This small rail with the rope was to secure sailors walking there over the gangway, the fast connection as narrow passage that joins the
quarterdeck to the
forecastle.
But there was usually no person for longer time, no real activities were necessary to do on top of the gangway.
And in worst case, the sailor would fall only some 2 or 2,5 meter down. So I would not install a net there.
At the bow it was much more important - falling into the sea was usually followed by the death of the sailor, only a small number of them were able to swim.
But this is only my opinion.
BTW: I will move this thread to a more correct area of the forum.......