I think the major difference here is between a layperson holding a communion service and a deacon holding a communion service. Both are permissible. A deacon, through his ordination, is an “ordinary” minister of Holy Communion like any priest or bishop whereas a layperson can only be an “extraordinary” minister of Holy Communion.
The issue here seems to be one of a deacon presiding at a communion service. People need to realize that deacons existed well before Vatican II. In fact, deacons existed before priests. People have this negative ideal that comes in two different groups - 1) that deacons are mini-priests and thus want to do what priests do, or 2) people don’t know what deacons do or why they exist so I am critical of them. This needs to be overcome through a better understanding of the diaconate.
In the deacon’s faculties that are granted him from the bishop upon his ordination, it states what he is allowed to do inside the bishop’s (arch)diocese. These normally include assisting at Mass, reading the Gospel, preaching, witnessing marriages, baptizing infants, etc. I also believe that communion services are part of this list. Now, the deacon’s pastor has to approve all actions that happen in his parish - as he would have to do for his associate pastors/vicars as well.
What the church does not want is the idea that priests are not needed - because they absolutely are needed. We cease being a Eucharistic Church without them. But, at the same time, people need to understand the reason for deacons and their function. Deacons presiding at a communion service, as they are when assisting at Mass, are present as “Christ the Servant” (in persona Christi diakonia). They are there to represent the people in service as Christ was. As we approach Holy Thursday, the washing of the feet is a perfect example of Jesus being the Servant. We must emulate Him and also “wash the feet” of those around us. In this service aspect, the deacon facilitates the uniting of God and His people. He does not do this through any act of consecration, but through the act of service at the altar - of allowing Jesus, found in the tabernacle, to be united to His people.
I think this also boils down to how God would want us to be in relationship with Him. God did not want to be locked up in the fancy temple after the exodus from Egypt. Instead He instructed to be placed in a tent in the center of the camp so that His people could be with him and him with them. A communion service, with the proper catechesis and reverence, is a beautiful way for God to be around His people, united with them in the Eucharist. If that could be done in the setting of the Mass, all the better, but don’t lock him away in the temple. And since a deacon’s actions are under supervision by his pastor, abuse of such a service should be few and far between.