Should we wipe the feet, or wash the feet?

In no place of the Qur'an does it say that we have to wipe our feet. However there are some interpretations given especially by the Shia that say that the feet are to be wiped. This is of course contrary to what has been revealed by Allah.

Secondly; the Prophet (ﷺ) to whom the Qur'an was revealed washed his feet and did not wipe them. Surely if the feet were to be wiped and not washed then the Prophet would have done so himself.

Thirdly; the Sahabah who were there while revelation occurred washed their feet and they didn’t wipe them. Surely if the feet were to be wiped then the best of generation would have wiped their feet.

Fourthly; the verse:[1]

"...بِرُءُوسِكُمْ وَأَرْجُلَكُمْ إِلَى الْكَعْبَيْنِ..."

- Take a look at the letters that are underlined. You will see that the seen is majroor, meaning it has a kasra (Ru'uSIkum) and the laam is mansoob meaning it has a fatha (Arjulakum). This indicates that the actions that are done on the head are different from what is done on the feet.

[1] [Qur'an 5:6]