I see it as beautiful when observed in a pure spirit. While we do this as a clergy thing, we involve the laity. But I see what the FW baptist do as wonderful. I'd even suggest people do this at home with the spouse and children.
This is not just about becoming humble. One can be humble and sad. This is finding joy in being a true servant. But we often miss the lesson taught to Peter. Allowing someone you feel is very special to wash your feet is the hard part of this lesson. Peter would have washed the feet of Christ in a New York second. Peter saw Christ as his Master. I would even think that Peter would have no issue washing the feet of any of Christ's flock at that time. But now Peter learns how to be served by the Master as well. Not just in His Glory but in a lowly way as well.
Without a doubt, Christ was teaching his clergy. Those who would set upon thrones. Those who had already asked which one was greater. Those who at this time still didn't get the concept of the Kingdom. Where the least of men is greatest and the greatest of men are least.