You may not have noticed that I am a member of a Lutheran congregation. I believe I can say with some certitude that Lutherans, even though they often disagree upon details from one set of Lutheran organizations to another, are most likely unanimous in failing to recognize foot washing as a sacrament. Certainly Luther did not include it in his very short list.
Yet Christ commanded it:
John 13
14If I then, your Lord and Master, have washed your feet; ye also ought to wash one another's feet.
The Catholic Church had a long list of what they considered were sacraments, but the Protestants filtered it down. Interestingly, using their criterion, Calvin added the sermon, footwashing, to the list. You can see his logic:
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The divergence of the Protestant churches from this definition and scheme was based on the fact that these proceeded on no settled principles. The notion that there are seven sacraments has no New Testament authority, and must be described as purely arbitrary; while the definition of a sacrament is still so vague that anything but an arbitrary selection of particulars is impossible. It is perfectly arbitrary, for example, to place Baptism and the Lord's Supper, which were instituted by Christ as ordinances of the church, in the same category with marriage, which rests not on His appointment but on a natural relationship between the sexes that is as old as the human race. While, therefore, the Reformers retained the term "sacrament" as a convenient one to express the general idea that has to be drawn from the characteristics of the rites classed together under this name, they found the distinguishing marks of sacraments
(1) in their institution by Christ,
(2) in their being enjoined by Him upon His followers,
(3) in their being bound up with His word and revelation in such a way that they become "the expressions of divine thoughts, the visible symbols of divine acts."
And, since Baptism and the Lord's Supper are the only two rites for which such marks can be claimed, it follows that there are only two New Testament sacraments. Their unique place in the original revelation justifies us in separating them from all other rites and ceremonies that may have arisen in the history of the church, since it raises them to the dignity of forming an integral part of the historical gospel. A justification for their being classed together under a common name may be found, again, in the way in which they are associated in the New Testament (Acts 2:41,42; 1 Corinthians 10:1-4) and also in the analogy which Paul traces between Baptism and the Lord's Supper on the one hand, and Circumcision and the Passover--the two most distinctive rites of the Old Covenant--on the other (Colossians 2:11; 1 Corinthians 5:7; 11:26).
It seems foot washing, as a topic, has been left out as irrelevant. Did forgetting of its significance, what it meant, lead to this omission?
An analogy is found in crime detection. A theft happened. The dog did not bark. Holmes found it puzzling, and interesting The police decided it was irrelevant. Did Holmes know something the police didn't? Homes knew that the reason the dog did not bark was because the thief was known to the animal. The police were ignorant or hasty in dismissing the relevance of this clue.
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Gregory (Scotland Yard detective): "Is there any other point to which you would wish to draw my attention?"
Holmes: "To the curious incident of the dog in the night-time."
Gregory: "The dog did nothing in the night-time."
Holmes: "That was the curious incident."[2]
The Adventure of Silver Blaze - Wikipedia
Maybe we believers are hasty in dismissing the relevance of the mention of footwashing, in leaving out considering it to be a sacrament, even though commanded by the Lord.
The Holy Spirit can bring to mind the significance of the words spoken by the Lord:
John 14
26But the Comforter, which is the Holy Ghost, whom the Father will send in my name, he shall teach you all things, and bring all things to your remembrance, whatsoever I have said unto you.
Baptism is the agreement to listen to the revelations from God. Foot washing is the promise to ask for daily bread. For edification. By prophesying and by discerning, filtering, like the Bereans. After you put that in your pipe, smoke it, absorb it and get your light bulb moment, we'll talk about what Communion means.