Are there any differences among these sentences?
So why would anyone use the exception-based loop in preference to the tried and true?
So why should anyone use the exception-based loop in preference to the tried and true?
So why shall anyone use the exception-based loop in preference to the tried and true?
These are contextually similar, and in many circumstances not mutually exclusive.
"Would" describes why a person might decide to do an action. It does not actually describe if an action is the best one, but it describes a person's internal motivations.
"Should" is more of an objective reason for why it is better to perform an action (rather than their other options).
If a person knows the best course of action, they probably "would" choose to do what they "should" do (i.e. Their knowledge that it is the best option causes them to decide to choose it).
"Shall" is rarely if ever used this way. It simply asserts that an action is going to be taken. It sounds very awkward, and "would" or "should" are much more common.
There is another distinction between "why would" and "why should" questions.
To ask: "Why would you do this?" is seeking the motive for such an action.
While: "Why should you do this?" is concerned with a duty or other obligation.
