In the book, The Temple Where Heaven Meets Earth (Deseret Book, 2008), Truman Madsen writes:
In the Gospel of John we read that in an upper room Jesus said to Peter that the acceptance of the ceremonial washing of feet was essential. Peter’s refusal would mean that “thou hast no part [elsewhere translated inheritance] with me” (John 13:8). That is strong language. Joseph Smith’s translation of the Bible notes that this washing “was the custom of the Jews under their law; wherefore, Jesus did this that the law might be fulfilled” (JST, John 13:10). Some scholars see this as a custom that Jesus replaced. In the Restoration, the washing of feet is both a preface to and an echo of sacred temple rites, a proper prologue to Jesus’ high priestly prayer in John 17 (which is a prayer for unity of Master and disciple as well as of disciple and disciple), and an example of subservience by a true and suffering servant. But it is more. It was given that they might “be clean every whit,” a condition which apparently neither their faith nor their baptism had thus far fully achieved (127).
If you are going to be clean, according to Joseph, you had better be in your regional temple for washing. Didn’t you know that is what Jesus was trying to teach on his last night with the disciples? Never mind his repudiation of the temple system in the earlier part of John’s Gospel.
Secondly, Truman states emphatically,
Jesus, in the book of John, as well as in the epistles of John, bears God’s name to the point that He can say, “the Father and I are one” (John 10:30. Does this mean their names are one? The specific divine name that is assumed in these passages is a matter of controversy. Perhaps it is the divine name in Exodus 3:14: “I am.” But the Masoretic text can be read to mean “I will become what I will become.” This is compatible with the view that Yahweh became the messianic figure of the New Testament. But it is incompatible with the philosophical thesis that God is exclusively “being” without the dimension of “becoming” (148, emphasis mine).
Plato’s god? Yes. The Christian God? No.
Jesus in Idaho Falls 
See Bryce’s post on this subject at Washing of Feet for additional information.
McConkie has no idea, really, what he is writing about because Joseph Smith completely missed the powerful drama in John 13.
Just for starters, does McConkie think that Jesus just passed right over Judas that last night by saying this?
It is not done before the world or for worldly people.
Also, secret ordinances are a bunch of hogwash.
It is alright to do ordinances before the world. They are Gospel ordinances.
(And I am curious. How are the LDS restoring washing. Footwashing has been going on for quite a while, though I don’t recognize it as the service that it once was – I don’t wear sandals. Christian brothers and sisters don’t have to literally wash my toes to show they are following the example of Christ. Of course, if anyone wants to give me a foot massage, I will readily accept the offer.)