Should foot-washing be a sacrament?

i) It's just a matter of arbitrary ecclesiastical tradition that it's not a third sacrament (or church ordinance, if you prefer).

ii) It has been incorporated in the Maundy-Thursday services of some liturgical denominations. In addition, some Pentecostal and Anabaptist denominations practice foot-washing.

iii) It is possible to practice the rite pridefully. "We honor the Lord's command, unlike all those other disobedient denominations!"

iv) Strictly speaking, Jn 13:1-17 is not a direct command to Christians generally, but a command to the disciples in the Upper Room. Not all commands addressed to the disciples are applicable to Christians in general. On the other hand, it would be too facile to say that no commands addressed to the disciples have a broader application. 

v) A basic problem is the difference between modern foot-washing and the original event. Back then, pedestrians used to walk barefoot or with open sandals on dusty, muddy, and (literally) crappy streets and dirt roads. In addition, the action of Jesus was spontaneous. The disciples had no advance notice.

By contrast, Christians who attend a foot-washing service know what to expect. Presumably, most of them wash their feet at home beforehand. Trim their toenails. Wear fresh socks. Deodorize their shoes. And drive to church. So the situation is almost diametrically the opposite of foot-washing at the Last Supper. It loses the original impact. 

vi) So I think the way to honor the principle exemplified by foot-washing is to apply that analogously rather than mechanically (literally). To take a hypothetical example, suppose a young Victorian aristocrat has a valet. Suppose his valet contracts TB–at the time a fatal and highly contagious disease. 

Normally, he'd die in a sanitarium (a kind of quarantine) or simply be kicked out, to die on the streets. But suppose the young aristocrat decides to personally care for his ailing valet. The consumptive valet is allowed to sleep in his master's bedroom. Indeed, in his master's bed. His master sleeps on a cot.

The master feeds, and bathes his ailing valet. Takes him to the bathroom. Cares for his terminal valet until the valet dies of TB. Reads the Bible to him. And collects from the BCP. All the while assuming the risk that he will be infected by TB through so much physical contact with his consumptive valet. 

That honors the meaning of the rite in a way that attending a Maundy-Thursday service does not. (Although  Maundy-Thursday service may be worthwhile for other reasons.)

vii) Of course, that's a hypothetical example. And not very realistic in a modern American context. Here's another example: suppose, during a high school football game, a player is seriously injured. He lives with his mom. During his convalesce, he needs help doing certain things–private things which would be humiliating to have his mom to perform. So some players on the opposing team volunteer to go to his house twice a day (morning and evening) to help him out. That's not embarrassing because it's man to man. That's analogous to the significance of foot-washing at the Last Supper. We should cultivate the habit of thinking about how to implement the foot-washing principle creatively.