First of all it is Allah's order in the qur'an to purify our selves in a certain manner in order to perform the prayer:
O you who have believed, when you rise to [perform] prayer, wash your faces and your forearms to the elbows and wipe over your heads and wash your feet to the ankles. And if you are in a state of janabah, then purify yourselves. But if you are ill or on a journey or one of you comes from the place of relieving himself or you have contacted women and do not find water, then seek clean earth and wipe over your faces and hands with it. Allah does not intend to make difficulty for you, but He intends to purify you and complete His favor upon you that you may be grateful. (5:6)
Allah gave us two different solutions:
- a general (and best) case (water is available),
- and an option under unfavorable conditions (no water is available or water would cause you harm). Which is the topic of this question and marked bold in the text quote above.
So we should stick to what Allah orders us and the prophet orders us as Allah further says:
It is not for a believing man or a believing woman, when Allah and His Messenger have decided a matter, that they should [thereafter] have any choice about their affair. And whoever disobeys Allah and His Messenger has certainly strayed into clear error. (33:36)
Now again as said in my earlier comment purifying or taharah for performing acts of worship is not equal to cleanness nor is najassah equal to uncleanness. You could clean yourself while performing wudu' or ghusl, but this is not the main goal, the main goal is to be in a pure state as Allah defined following his orders. If for example cleanness would be the goal, why is waste or excessive use of of water for ghusl or wudu' regarded as frowned upon?
As the quote I've falsely attributed to imam a-Shafi'i turned out a hadith or athar on the authority of 'Ali ibn abi Talib () here the full correct quote:
Narrated Ali ibn Abu Talib:
If the religion were based on opinion, it would be more important to wipe the under part of the shoe than the upper but I have seen the Messenger of Allah (ﷺ) wiping over the upper part of his shoes. (Sunan abi Dawod)
Shoe here refers to al-Khuff الْخُفِّ a leather sock.
What does this quote mean:
If the rules of Allah (the religion) would be based on the human logic and what a human would regard as fine neglecting what Allah and his messenger have ordered they would be otherwise. But then we would be in clear conflict, as on one hand we pretend being Muslims (follow Allah's orders) and on the other hand we act against his orders.
This report is qualified as sahih by at least ibn Hajar and al-Albani.