I'm not so much concerned with the reasoning around the duel (apart from why AK was needed to make someone dodge). I'm mainly against Quirrell taking the boy to Azkaban in the first place. General common sense says that is not a good idea unless it is a desperate situation. Especially since Quirrell can't cast magic on Harry if he decides to do something rash.

What is the expected utility of taking Harry to Azkaban in total, from Quirrells point of view?