Hi my two cents..
The washing of feet or the healing of feet represents bringing the gospel .In effect Christ said: If I do not wash your feet you do not have any confirmation of the gospel.. you have no part with me.
Feet are used to indicate the work of God. It indicates we are worshiping Him and not the feet that need the “water of the word” as one person referred to as an example..
Romans 10:15 And how shall they preach, except they be sent? as it is written, How beautiful are the feet of them that preach the gospel of peace, and bring glad tidings of good things!
In that way in various parables we can see the doctrine being developed.it was not just a good tradition of men used to sooth one pain, as a creature comfort..
Let a little water, I pray you, be fetched, and wash your feet, and rest yourselves under the tree:And I will fetch a morsel of bread, and “comfort ye your hearts”; after that ye shall pass on: for therefore are ye come to your servant. And they said, So do, as thou hast said. Gen 18:4
There I believe we can see the washing of feet to indicate the gospel with the morsel of bread to represent the word of God, our comfort to indicate the gospel in the Old testament.
Exodus 3:5 And he said, Draw not nigh hither: put off thy shoes from off thy feet, for the place whereon thou standest is holy ground.
There feet and holy ground are used to indicate the good soil the word of God in which the seed fell on.
And it came to pass by the way in the inn, that the LORD met him, and sought to kill him.Then Zipporah took a sharp stone, and cut off the foreskin of her son, and cast it at his feet, and said, Surely a bloody husband art thou to me.So he let him go: then she said, A bloody husband thou art, because of the circumcision. Exo 4:24
In that case according to that parable which is historically true at the same time we see the meaning of circumcision in respect to Christ, our bloody husband in effect pouring out his blood on Moses feet, the gospel of his salvation.
1Sa 2:9 He will keep the “feet of his saints, and the wicked shall be silent in darkness; for by strength shall no man prevail.
There the gospel is shown as that which keeps us in Christ.
Revelation 3:9 Behold, I will make them of the synagogue of Satan, which say they are Jews, and are not, but do lie; behold, I will make them to come and worship before thy feet, and to know that I have loved thee.
There again He refers to feet as brining the gospel to prove to the un believer he does love us.