I should also note that this is all just an illustration of how players in the NFL have become more specialized over time.
Before around 1960, it was uncommon for a team to have a player who only handled kicking or punting duties – these were nearly always handled by a player who normally played another position. (Lombardi’s early Packer teams had guard Jerry Kramer or halfback Paul Hornung doing the kicking, and ends Max McGee or Boyd Dowler doing the punting.)
As the 1960s went on, teams started using full-time specialists, and some of those players did, indeed, act as both kickers and punters.
But, at that same time, soccer-style placekicking emerged in the NFL. Most of the early soccer-style kickers were, in fact, soccer players (frequently from Europe), who had not played American football at all before coming to the U.S. as kickers; while they took over the kicking game in the NFL over the course of the 1960s and 1970s, very few (if any) of them wound up becoming punters.
Your typical NFL team in the early-to-mid 1970s had a placekicker who was probably originally a soccer player, may not have been born in the U.S., and had limited experience with punting a football. Thus, despite the fact that the teams were committed to fielding full-time specialists, there weren’t many top-of-the-line kickers who were also top-of-the-line punters…and, so, they had separate roster positions for kickers and punters.
By the late 1970s and early 1980s (Erxleben’s era), American-born soccer-style placekickers were entering the league in force, and (obviously) some of them had been both kickers and punters in college. The few experiments such as Erxleben’s that NFL teams tried failed miserably, and I suspect that they helped cement the conventional wisdom that the two jobs should be handled by separate players.
One thing that the specialization has done is led to far greater accuracy in the kicking game, and far greater distances in the punting game. Up until the 1970s, NFL kickers typically succeeded at ~60% of their field goal tries, and ~90% of their extra-point tries. Today, a kicker who had those sort of numbers would be very quickly out of a job – the modern averages are over 80% for field goals, and 99% for extra points. Similarly, in the 1970s, punters averaged around 40 yards per punt; today, it’s around 45 yards.