The Minotaur was certainly the son of the Queen of Knossos, and possibly the grandson of Poseidon, the patron of Crete. You cannot just sling such a being in a cell; building a separate wing of the palace for him (specially designed for him by the leading architect Daedalus and visited at regular intervals by the best and brightest young people of Greece) sounds much better.
Royalty, by definition, is not treated like the rest of the population when it comes to crime or disease; there was a twentieth-century story of the 'Monster of Glamis', allegedly a member of the British Royal Family born with terrible mental and physical defects who was confined to Glamis Castle for life. The story had almost nothing behind it: what credibility it had came from the undoubted fact that if such a child had been born, it would certainly not have been been put in a normal asylum or seen in public.