There are psychological reasons that it's there and that it's important. I remember when, running through the woods at age 10, I fell and scraped my palm quite badly on a rock, embedding tiny bits of gravel. They had to come out, so my grandmother, using a needle, dug them out. She was as careful and gentle as she could be, and I didn't make a sound, but the pain of it made me pass out. When I awoke, my unconsciousness frightened me and lowered my inhibitions so much that I burst into tears, much to my embarrassment.
Foot washing is like that.
Because it's unusual, because it's embarrassing, it breaks something open in us, lowers our inhibitions, opens doors to the soul so that God's Spirit can flow in. This spiritual opening to God's grace can be easily missed if we chat and laugh during the service, or focus the mind on other things. But to do that is to miss a wonderful blessing. The Holy Spirit quickens the sensibilities of those who follow the example of their Lord. Roots of bitterness that have crowded out the precious plant of love are made manifest.