I don't think it was ever considered that they were in some way entering the clergy (deacon-priest-bishop), which was and is distinct.
Excellent point!
"As I understand it, in the days of St. John Chrysostom etc. there were deaconesses whose role was catechizing and baptizing women. This was because men could not respectable visit women in their homes and then confer the sacrament of Baptism, which was done naked. These deaconesses also visited the sick, brought alms to the poor, and other wise participated in charitable work."
Indeed there were. They also brought communion to the sick, catechised grown women and nursed sick women.
"I don't think it was ever considered that they were in some way entering the clergy (deacon-priest-bishop), which was and is distinct."
Actually, they were considered "clergy" and went through what was called an ordination, using the same word in Greek as describes ordination to the diaconate for men. It is vitally important to remember, however, that this order of the clergy was specifically designed to fulfill strictly circumscribed functions, was limited to older unmarried women, usually widows and was not at all seen as a step towards the priesthood. The Holy Synod of the Church of Greece recently voted to reinstitute the order on a limited basis with the traditional functions.