I am surprised by your statement that this doesn’t happen on your F. Because I believe that is exactly how my F behaves. I will try later today.
As a workaround, you could always dedicate one custom setting to “everything on zero”.
Third party options of adapter ring that screw onto the lens combined with a good UV- or protection filter work just as good. I believe JJC has a good one. Make sure the optional lens hood works with a bayonet. That's easier than a filter thread screw-in one.