Is it permissible to refrain from praying behind an imam who does not recite well and does not accept advice, and is it permissible for him to displace someone who recites well to lead the people? And what should a Muslim do concerning this matter?

It is not permissible for someone in the mosque who has not yet prayed the obligatory prayer to absent himself from the congregational prayer if the prayer of their Imam is sound and his recitation is sufficient. This is because congregational prayer is obligatory for anyone present in the mosque, and the Prophet, peace and blessings be upon him, commanded anyone who prayed at home and then attended the congregational prayer at the mosque to pray with them.

As for removing someone who has come forward to lead the prayer after the iqamah, this should not be done. The one who came forward first—if appointed by the Imam—has more right to lead the prayer. If he was not appointed, then the one whom the people of the mosque approve should be put forward. No one has the right to impose himself on the worshippers.