I will play the Geezer card to bring up the name of Tommy Davis, who was both the punter and placekicker for the 49ers from 1959 to 1969.

Davis led the NFL in field goals made in 1960, kicking 19.  He went to the Pro Bowl in 62 and 63.  Tommy Davis led the league in punting in 1962 with a 45.6 yard average (before they kept net average).

You don't see double-duty kicker/punters any more.