Because of the saying of the Prophet (peace and blessings be upon him): "The people should be led in prayer by the one who is the best reciter of the Book of Allah (the Holy Qur'an)."
And a disbeliever's performing the prayer does not become proof of his being a Muslim unless he verbally declares Islam before the prayer.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / Q5141
Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) says that the Messenger of Allah (peace and blessings be upon him) said: "I have been commanded to fight the people until they testify that there is no god except Allah and that Muhammad (peace and blessings be upon him) is the Messenger of Allah, establish the prayer and pay the zakah. When they do these things, they have protected their blood and their wealth from me, and their reckoning is with Allah."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 5141
Sayyiduna Anas bin Malik (may Allah be pleased with him) says that the Messenger of Allah (peace and blessings be upon him) said: "I have been commanded to fight the polytheists until they testify that there is no god except Allah and that Muhammad (peace and blessings be upon him) is the Messenger of Allah. When they have testified that there is no god except Allah and that Muhammad (peace and blessings be upon him) is the Messenger of Allah, prayed as we pray, faced our qiblah and eaten our slaughtered animals, then their wealth and their blood are forbidden to us, except by its right. For him are the same rulings as for a Muslim, and upon him is the same as is upon any Muslim."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 5142
Urwah bin al-Mughirah bin Shu'bah narrates from his father, Sayyiduna al-Mughirah bin Shu'bah (may Allah be pleased with him), who said: The Messenger of Allah (peace and blessings be upon him) stayed behind, and I stayed behind with him. When he (peace and blessings be upon him) had relieved himself, he said: "Do you have water?" I brought a water vessel, and he (peace and blessings be upon him) washed his face and his hands. Then he (peace and blessings be upon him) began to pull his jubbah back from his forearms, but the sleeve of the jubbah was tight, so he (peace and blessings be upon him) took his hand out of the jubbah, put the jubbah over his shoulders, washed his forearms, and then wiped over his forelock, his turban and his leather socks. Then he (peace and blessings be upon him) mounted, and I mounted too, and we reached the people who were praying. Sayyiduna Abd al-Rahman bin Awf (may Allah be pleased with him) was leading them in prayer, and one rak'ah had already been completed. When he sensed the arrival of the Prophet (peace and blessings be upon him), he began to step back, but he (peace and blessings be upon him) signalled to him, so he himself led the prayer. When he gave the salam, the Prophet (peace and blessings be upon him) stood up, and I stood up too, and we prayed the rak'ah that we had missed.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 5143