The dear departed was invariably picked to have his feet washed; being male, being a solid member of whichever parish we were in and being someone who would not say "no". He hated it; trying to find decent socks, shoes that he could easily get off and on with arthritic fingers, making sure his toenails were decent and making sure he put out his left foot only, he didn't want any priest to be startled by his hammer toe on the right foot. We'd never start that Mass in the right frame of mind, he'd be worrying too much, and he a server of some standing, proficient in both rites. This was different, it was about him as a man, not a server, and he simply hated the attention.
Thought (1): It is disruptive to the congregation.
My old Novus Ordo Missal says the following:
The washing of the feet may follow the homily. The men who have been chosen are led by the ministers to chairs prepared in a suitable place. The priest goes to each man. With the help of ministers, he pours water over each one's feet and dries them.
Thought (2) : that word "may"... it is optional, remember that, it is optional
Thought (3): those words "suitable place".... I maintain the sanctuary is NOT a suitable place. My first parish in Salford was blessed with a very large sanctuary, but the priest (no Trad) always insisted that chairs were positioned infront of where the altar rails would have been, had they not been removed. He said, "it is about serving the people of God, and that takes place outside the sanctuary, we serve God in the sanctuary". He had a point, and I happen to agree with him. Indeed, I've been informed that if this ever takes place in the Orthodox liturgy, it obviously happens on the layman's side of the iconostasis. I would also argue that hospitals, prisons etc are suitable places. The Mandatum could be seen as "liturgy in the streets" in a way that no other aspect of the liturgy can.
Thought (4): you don't need 12, but you knew that already
Thought (5): If women are permitted, women are permitted, deal with it. However, this woman won't be volunteering. Having been privileged enough to receive the Sacrament of the Sick in the old rite where one's feet are anointed with the sacred oil... oh dear no! Priests and women's feet, it is too intimate... I actually kept my shoes on and he did a double anointing on both hands instead... we were both uncomfortable about the intimacy of seeing my feet, that felt right, I was not about to expire, I was not on my death bed, though the sacrament was absolutely necessary, undressing before him would have been wrong. It was unsaid, we both just knew that naked female feet were not appropriate.
Is it actually "liturgy" at all? It could be argued that it is a form of preaching, and before Pius XII, was not preaching seen as a non-liturgical act? Indeed, just like the maniple is removed before the homily and the homily takes place outside the sanctuary because it is not a liturgical act, there is no maniple for the washing of the feet, there is a REAL TOWEL. Hmmm.....that says to me it was originally not intended to be liturgical.... therefore it can be performed anywhere and on anybody as an act of symbolic service to God's people by priests, mother superiors, bishops, popes.... just not in the sanctuary... because it is non-liturgical. BUT we are in a mess because preaching is considered to be a liturgical thing these days and the maniple is not worn in the new rite.
If it is just a re-enactment of Christ's symbolic act of service to the Eleven, then surely it should only be performed by a Bishop on priests (and probably only in a Cathedral). It is a heirarchy thing, and if it is clerical, then it is clerical and laypersons should not be used, especially to "represent" the priesthood.
I now attend a 12 noon Mass on Holy Thursday because I have become so uncomfortable with seeing the Mandatum take place in the sanctuary. The noon Mass has no Mandatum and I then return to the church for the stripping of the altar and watching in the evening.... it is the stripping of the altar that sends the shivers down my spine.... and to me, it is that act that is the essence of that special day.