"Respectfully, what is
the purpose of the rim liner in our Model A wheels?"
They protect you from the fear of what could happen if you didn't have them.
Actually the original wheels had thick paper liners, and I have an original liner still on one of my wheels. Sometimes the electrically welded spokes left a little spike of sharp steel that could poke a hole in the tube. If your rims have no rough spots from rust and no weld spikes, then you probably have no need for the liners.