No.

Just because no AFCIs are available does not mean they are obsolete or "defective". Codes are not grandfathered so there is no mandatory reason to have to install AFCIs. Why would they need to "be upgraded to the safety standards required of current installations"?? That would be a service change IMO.
If a renovation is done that is another story.

Pushmatics were very good breakers in their day and you can still get replacements. Replacing a breaker would NOT demand an AFCI either. It is the circuit that requires AFCIs, and replacing a breaker is NOT altering the branch circuit.
About the only thing I don't like is that very old ones, or ones that are in a harsh environment, have the tenancy to not reset. I have never had an issue where they would not trip or shut off.