The account of the Last Supper was done in the context of a sacred liturgical act, the Passover. Jesus was instituting the new and everlasting covenant, a covenant that would be sealed in His Blood. He was charging the 12 (actually, from the looks of it, it’s the remaining 11, with Matthias to come later, but, that is another story) with doing the same. Doing the same meant that they would have to be ordained. Here, Jesus was the new Aaron, offering the new sacrifice and instituting a new priesthood. That is also why, in some locations, the Chrism Mass is also celebrated on Holy Thursday to show the intimate connection between the Holy Sacrifice of the Mass and the bishops and priests. Of course, in our case, it usually falls on a Tuesday, but, that still does not diminish the meaning.
While there are layered meanings to the washing of the feet, Jesus places this within the confines of the Last Supper. As I noted in the paragraph above, the Aaronic priests had to purify themselves before offering the sacrifice. Jesus, because He is all pure, did not need this purification ritual. The Apostles, on the other hand, did. And, since they were going to be charged with perpetuating this sacrificial offering of the True Paschal Lamb (Do this in memory of me), they needed to be purified.
Yes, I realize that there is the connection of service. However, the priest, in persona Christi, is to be the servant of all. Every day that he offers Mass he is persona Christi. This particular ministry is demanding because as John the Baptist predicted, “He (Jesus) must increase and I must decrease.” Even the bishops, who are the successors of the Apostles, must be the servants of their dioceses. They are called to serve their flock, feeding them and tending them. A priestly vocation, lived correctly, involves emptying oneself and allowing Christ to completely take over.
One of the titles of the Supreme Pontiff is “servant of the servants of God.” That is why Jesus made it perfectly clear to Peter, the man he chose to be his Vicar, that if he did not get his feet washed, he would have no part of Jesus’ ministry.
Remember what Jesus also told Peter when Peter asked him to wash the rest of him as well his feet. He said that those who have bathed do not need to be bathed again, although not all are pure. He was referring here to Judas. Thus, Judas, even though his feet had been washed, did not have that purity of heart.
If we examine the ritual very carefully, the priest removes his chasuble, the symbol of his office (along with the stole) and washes the feet of the 12 men. The Holy Father goes a step further. He removes his chasuble and wears the dalmatic, the vestment proper to the deacon. The deacon’s original duty was to serve the community, tending to the widows and the orphans (this dates back to the Acts of the Apostles). His office is at the lower rung of the major orders (diaconate, prebyterate, episcopal). The Pope (and all bishops) possess the fullness of the priesthood, but, on Holy Thursday, the Pope assumes the role of servant, which is to say, that of the deacon.
It is not so much that we are doing a historical re-enactment. Even the portion of Eucharistic Prayer I refers to the Last Supper in the present tense, using the word today. We are not just living a moment in history. The celebrant is fulfilling what Jesus told the Apostles to do.
I just think that when we start to tool around with the rituals just because of some misguided notion, we wind up watering down the meaning. Yes, service is involved here. But, it is at a much deeper level. It winds up going back to the celebrant and his daily decreasing of himself so that Christ may increase through him. So then, the words of St. John the Baptist are the words of the celebrant, too, and those of every bishop and priest, “He must increase while I must decrease.”
There has been much made about a 1987 statement made by the USCCB regarding just whose feet may be washed. Paschale Solemnitatis cleared that up a year later, specifically stating that it is the feet of the 12 chosen men that are to be washed.