I disagree with the Pilate analogy. The washing of hands holds other meaning as well, though I don’t necessarily believe it is the case in which the OP refers. I have a slight hunch that it is so more people, including women, can be included. The USCCB is clear on the practice of washing on Holy Thursday. First, here is a bit on hand washing:
In biblical times it was prescribed that the host of a banquet was to provide water (and a basin) so that his guests could wash their hands before sitting down to table. Although a host might also provide water for travelers to wash their own feet before entering the house, the host himself would not wash the feet of his guests. According to the Talmud the washing of feet was forbidden to any Jew except those in slavery.
In the controversies between Hillel and Shammai (cf. Shabbat 14a-b) Shammai ruled that guests were to wash their hands to correct “tumat yadayim” or “impurity of hands” (cf. Ex 30, 17 and Lv 15, 11). Priests were always to wash their hands before eating consecrated meals. The Pharisees held that all meals were in a certain sense “consecrated” because of table fellowship.
Jesus’ action of washing the feet of his disciples was unusual for his gesture went beyond the required laws of hospitality (washing of hands) to what was, in appearance, a menial task. The Lord’s action was probably unrelated to matters of ritual purity according to the Law.
Perhaps this practice mentioned in the OP is a skewed interpretation of washing the hands before the consecrated meal?
The rubric for Holy Thursday, under the title WASHING OF FEET, reads:
“Depending on pastoral circumstance, the washing of feet follows the homily. The men who have been chosen (viri selecti) are led by the ministers to chairs prepared at a suitable place. Then the priest (removing his chasuble if necessary) goes to each man. With the help of the ministers he pours water over each one’s feet and dries them.”
*]The Lord Jesus washed the feet of his disciples at the Last Supper as a sign of the new commandment that Christians should love one another: “Such as my love has been for you, so must your love be for each other. This is how all will know you for my disciples: by your love for one another” (see John 13, 34-35). For centuries the Church has imitated the Lord through the ritual enactment of the new commandment of Jesus Christ in the washing of feet on Holy Thursday.
*]Although the practice had fallen into disuse for a long time in parish celebrations, it was restored in 1955 by Pope Pius XII as a part of the general reform of Holy Week. At that time the traditional significance of the rite of foot washing was stated by the Sacred Congregation of Rites in the following words: "Where the washing of feet, to show the Lord’s commandment about fraternal charity, is performed in a Church according to the rubrics of the restored Ordo of Holy Week, the faithful should be instructed on the profound meaning of this sacred rite and should be taught that it is only proper that they should abound in works of Christian charity on this day."1
*]The principal and traditional meaning of the Holy Thursday mandatum, as underscored by the decree of the Congregation, is the biblical injunction of Christian charity: Christ’s disciples are to love one another. For this reason, the priest who presides at the Holy Thursday liturgy portrays the biblical scene of the gospel by washing the feet of some of the faithful.
*]Because the gospel of the mandatum read on Holy Thursday also depicts Jesus as the “Teacher and Lord” who humbly serves his disciples by performing this extraordinary gesture which goes beyond the laws of hospitality, the element of humble service has accentuated the celebration of the foot washing rite in the United States over the last decade or more. In this regard, it has become customary in many places to invite both men and women to be participants in this rite in recognition of the service that should be given by all the faithful to the Church and to the world. Thus, in the United States, a variation in the rite developed in which not only charity is signified but also humble service.
*]While this variation may differ from the rubric of the Sacramentary which mentions only men (“viri selecti”), it may nevertheless be said that the intention to emphasize service along with charity in the celebration of the rite is an understandable way of accentuating the evangelical command of the Lord, “who came to serve and not to be served,” that all members of the Church must serve one another in love.
*]The liturgy is always an act of ecclesial unity and Christian charity, of which the Holy Thursday foot washing rite is an eminent sign. All should obey the Lord’s new commandment to love one another with an abundance of love, especially at this most sacred time of the liturgical year when the Lord’s passion, death, and resurrection are remembered and celebrated in the powerful rites of the Triduum.[/LIST]
The washing of hands is, in my view, silly. That is unless someone can show me a reason to believe otherwise