I would like to add one bit to the conversation.
I was recently speaking to a few members of a religious order in my Diocese that exclusively use the Extraordinary Form, as well as their chaplain. I didn’t know what to expect when the subject came up, so I was surprised to hear that one of the sister’s father was a permanent deacon.
In this conversation, it became apparent that few members had any issue with permanent deacons per se, but that the greater issue was with how permanent deacons were formed, or how they ministered.
In the Extraordinary Form, the role of the deacon is similar to that of a deacon in the Byzantine tradition—the deacons role is in assisting the priest. In this way, the deacon would not minister liturgically as an individual, but always do so in the presence of a priest while acting as his assistant. This is especially prevalent in the Byzantine tradition, in which a deacon is not even suppose to vest without a priest’s blessing.
In this way, my interlocutors were very fond of the idea of a permanent deacon—Fr. Chaplain even opined how wonderful it would be if they had one there, that way he could offer Missæ Solemnes more often.
A shift occurred when the office of deacon was brought into the Ordinary Form. Whereas previously it appears that the deacon was an assistant, in the rituals related to the Ordinary Form a deacon can assume a presidential role (presiding at Baptisms, Vespers, Marriages, et c).
I’m unsure of how this principle relates to the Extraordinary Form of the Roman Rite—Although it seems that a deacon certainly could Baptize and witness Marriages, I’m not sure if a deacon ever would before the 1970’s. Additionally, a cursory glance at a few rubrical texts don’t mention any possibility of a deacon presiding at the Liturgy of the Hours.
The idea of a deacon presiding at anything is very much foreign to Byzantine liturgical thought, and I’ve needed to explain this to several curious Orthodox priest-friends. From my understanding, some Churches have allowed deacons to preside at the Liturgy of the Presanctified, but this is hotly debated.
Finally, to interject my own opinion on the matter: I very much like the idea of a deacon assisting the priest in Sacramental situations—I think it better manifests the hierarchical nature of Christ’s Church. Better yet, let another deacon, or a subdeacon, also assist to show forth a Trinitarian symbolism. That having been said, I also quite like the idea of a deacon being able to assume a presidential role at something like Vespers. It allows for a community to pray liturgically when a priest is not available.