T.S. Eliot used verse for “Murder in the Cathedral” for several reasons.
First, dramas were written in verse long before they appeared in prose. Classical, medieval, Elizabethan, and Jacobean drama were all in verse.
Eliot felt that prose was ideally a purely intellectual and reflective medium and that verse synthesized the intellectual, emotional, and aesthetic components of language. He considered that the growth of prose, especially as manifested in the scientific prose of the Royal Society and what he saw as the anti-intellectualism of Romantic verse, caused our intellectual and emotional sensibilities to split (the “disassociation of the sensibility”). By writing the drama in verse, set in the past, he was trying to recover an approach to religion which balanced emotional, spiritual, and intellectual.