What is the wisdom behind stipulating purity for prayer, unlike other acts of worship?

Allah Almighty commanded purity for prayer and wearing the best clothes, as He said: "O you who have believed, when you rise to [perform] prayer, wash your faces..." and the Prophet, peace and blessings be upon him, said: "There is no prayer without purification."

Imam Al-Kasani explained some of the reasons for this: 1. Reverence and Service: Prayer is serving and revering the Lord. Standing before Allah with a pure body, garment, and place is more effective in showing reverence and more complete in service, just as ritual impurity (hadath and janaba) is a spiritual defilement that causes disgust. Furthermore, the limbs of ablution are usually not free from dirt, and washing them purifies them. 2. Purification of the Inner Self: Allah commanded the washing of outward limbs as a reminder to purify the inner self from deceit, envy, arrogance, and ill-suspicion, as these are causes of sins. 3. Gratitude for Blessings: Washing these limbs is an expression of gratitude for the blessing of their existence, as they are means to attain great blessings (the hand, the foot, the face, and the head with its senses). 4. Expiation of Sins: Washing the limbs is an expiation for the sins committed by them, as most sins are committed through them (such as taking what is unlawful, walking towards what is unlawful, looking at what is unlawful, eating what is unlawful, and listening to what is unlawful). Narrations have been transmitted stating that ablution is an expiation for sins.

It must be noted that the issue of requiring purity for other acts of worship besides prayer (such as circumambulation and touching the Qur'an) is a matter of scholarly disagreement.