Your Old Chicago is a prime candidate for a protector. It will smooth the edges of the old mylar, keep new dirt from collecting around the edges of the old mylar, reduce future wear on the playfield and smooth your inserts.
I make mine own and always leave the plastic under one post near the top. Only one, so that the plastic can expand and contract in all directions. The protectors never move even when I lift the playfield.
After cleaning the playfield, I usually put a spray wax on before the protector. Probably doesn't need it, but it doesn't hurt.