Here's my real-world workflow where only a sync Ajax worked for me. Not saying it can't be rearranged to allow an async. (For the record, i did read the original ticket closely enough to know you're not wagging a finger at sync Ajax calls...) ;)
My application lets a user enter a customer name, and when they select the customer, info is pulled in from a 3rd party database, populating a form. The purpose is this data is submitted & pushed to a different system, but allows my user to edit data if necessary & add a couple required values the original data doesn't track.
The user isn't allowed to edit certain values (financial info), so if the source is invalid, they have to go back & fix it there. To deter edit attempts, the inputs are set to read-only. Once the user has filled in the additional info, they submit. The form is validated using Validation, with one field that MUST be verified against a different database. If it's invalid, the submit should fail & force the user to fix the value in the original source.
Since the value is validating in the submit event via Ajax, i can't use async because the submit action will proceed before a response is received. My sync request checks the value and sets an event-level (set within the event handler, but outside the Ajax call) boolean. That and the rest of the form validation determine whether the submit event continues.
As i've typed this up, i can think of a couple other places where i will try to fix this race condition, but it's an example of where sync requests would be legit & necessary barring alternate solutions.