Is it obligatory to wash your feet every day?

Maimonides (Tefila 43) rules that before the Shacharit prayer one must wash “one’s face, hands, and feet.”
The latter speculate that it originates from Shabbat (n) “A man washes his face, hands, and feet every day for his salvation, because it is said, and every work of the Lord is for his benefit” or from Cholin (kv.) which deals with washing hands in the morning in the waters of the Tiberias hot springs. Rabbi Yochanan says there that one may immerse oneself in the waters of the Tiberias hot springs, but not wash one’s face, hands, and feet. This implies that one must wash one’s feet before praying.
This law is also stated in the Siddur HaGeonim and in the Witri Machzor.
From the Gemarat it does not clearly appear that there is an obligation specifically before the morning prayer, but apparently there is an obligation every day to wash the feet.
Does the Rabbi think there is such a halakhic obligation? Or is there another, more plausible possibility?
Thank you very much!