Why did foot washing become a common practice in Christianity?

Sacrament

Outward sign of an inward grace.

John 7:38 Whoever believes in me, as the Scripture has said, streams of living water will flow from within him."

John 4:14 but whoever drinks the water I give him will never thirst. Indeed, the water I give him will become in him a spring of water welling up to eternal life."

It has the same connotation as the Eucharist:

John 6 :53 Jesus said to them, “I tell you the truth, unless you eat the flesh of the Son of Man and drink his blood, you have no life in you. 54 Whoever eats my flesh and drinks my blood has eternal life, and I will raise him up at the last day. 55 For my flesh is real food and my blood is real drink. 56 Whoever eats my flesh and drinks my blood remains in me, and I in him. 57 Just as the living Father sent me and I live because of the Father, so the one who feeds on me will live because of me.

John 13:8 "No," said Peter, "you shall never wash my feet." Jesus answered, "Unless I wash you, you have no part with me."

Ephesians 5:25-27 NET Husbands, love your wives just as Christ loved the church and gave himself for her to sanctify her by cleansing her with the washing of the water by the word, so that he may present the church to himself as glorious – not having a stain or wrinkle, or any such blemish, but holy and blameless.

In Scripture, words like water, bread, wine, chicks, children means interpretation of Scripture. Israel was given Scripture, the vineyard, and expected to ”harvest” life giving wine from it:

Matthew 21:33-35 NET “Listen to another parable: There was a landowner who planted a vineyard. He put a fence around it, dug a pit for its winepress, and built a watchtower. Then he leased it to tenant farmers and went on a journey. When the harvest time was near, he sent his slaves to the tenants to collect his portion of the crop. But the tenants seized his slaves, beat one, killed another, and stoned another.

Man shall not live by (physical) bread alone? This parable was told right after the Pharisees were informed that prostitutes and tax collectors would enter the kingdom of God before they themselves would.

Its parallel is here:

Matthew 23:37 NET“O Jerusalem, Jerusalem, you who kill the prophets and stone those who are sent to you! How often I have longed to gather your children together as a hen gathers her chicks under her wings, but you would have none of it!

Bread and wine is the Word of God, metonym for Message, which is the meaning, revelation, interpretation of Scripture:

John 5:39 NET You study the scriptures thoroughly because you think in them you possess eternal life, and it is these same scriptures that testify about me,

1 Corinthians 10:4 NET and all drank the same spiritual drink. For they were all drinking from the spiritual rock that followed them, and the rock was Christ.

The ordinance had its start when Jesus commanded it after the two meals, the supper they ate before the instituion of the Lords supper also called a love feast.

But we should know that Christ made a comment that sense we were already bathed(completely clean) we only need to wash our own feet, sense even though declared clean would be dirtied in our spiritual walk being imperfect. The bathing represents our one time ordinance of water baptism but will still need to wash only our feet to be cleansed of all unrighteousness and that is to continue to confess our sins for forgivness. In this comment we were not commanded to literally wash our feet for this cleanse.

But what was commanded as we are not greater than our Master and Teacher to not do as He did to us as an act of humility but service. jesus came to serve and humbled himself to fulfill the righteousness of the Law even showing humility on a cross.

So washing eachothers feet is commanded as He washed ours to remind us of our humilitt to eachother and service to regard ourselves lower than eachother.

So like the physical elements in water baptism, lords supper, Long and short hair in coverings and uncoverings, so also in foot washing thier is spiritual meaning for remembrance of how we should act in the presence of each other, strangers,God and angels bit akso remember what God has one for us. All these 4 ordinances are commanded by Jesus and handed down by Christ and His Apostles.

The act of washing feet predates the Reformation. It was encouraged of the abbot of a Benedictine Monastery to wash the feet of guests by the Order of St. Benedict(c. 530). The washing of the feet is done yearly in the Roman Catholic Church.

I do not know what all denominations practice the washing of feet.

For more information, you can read about it in the Catholic Encyclopedia:

The liturgical washing of feet (if we can trust the negative evidence of our early records) seems only to have established itself in East and West at a comparatively late date. In 694 the Seventeenth Synod of Toledo commanded all bishops and priests in a position of superiority under pain of excommunication to wash the feet of those subject to them. The matter is also discussed by Amalarius and other liturgists of the ninth century. Whether the custom of holding this "maundy" (from "Mandatum novum do vobis", the first words of the initial Antiphon) on Maundy Thursday, developed out of the baptismal practice originally attached to that day does not seem quite clear, but it soon became an universal custom in cathedral and collegiate churches. In the latter half of the twelfth century the pope washed the feet of twelve sub-deacons after his Mass and of thirteen poor men after his dinner.