The minor order of Exorcist was instituted in the third century to assist the higher clergy with the initiation of converts from paganism, who were not infrequently under demonic influence. These men performed exorcisms before or during baptisms, and provided general care for persons afflicted with evil spirits. Other minor clerics assisted the clergy with other functions, and their office was generally a permanent vocation (rather than a stepping stone towards the priesthood).
As Christianity spread, paganism subsided (not completely but to a large extent in areas inhabited by Christians), and so demonic possession also became less common. The minor order of Exorcist no longer in high demand, it became, along with the other minor orders, a transitional state on the way to becoming a priest; and the authorization to perform a solemn exorcism was limited to the higher clergy. Although “minor exorcists” were still ordained, theirs was a bound power, as it remains today, which means they have the power in principle, but cannot use it until they reach priestly ordination, and then only with authorization from the bishop.
Part of the value of having minor orders, even with bound powers, is that it prepares the candidate for the priesthood by gradual steps. His responsibilities increase and bring him closer and closer to the altar and the Holy Eucharist. As noted above, the minor orders – and subdiaconate – are still in use, with approval from the Holy See, by societies of apostolic life that use the traditional Roman missal, such as the FSSP.