One concern I have with ARIA use without structural supports is that these accessibility benefits will be limited to users of screen readers. For example, if ARIA headings placed on divs are used to meet WCAG conformance - the indication of headings will not be apparent to a user with custom style sheets - unless CSS selectors are used to account for ARIA roles
[Joe Chidzik] It is good practise to use appropriate HTML elements first, and then fall back to ARIA for modifying an existing element if a suitable HTML element does not already exist. In this case, the standard h* HTML elements exist for headings, and should be used in preference to a div+aria heading code. Of course, standard HTML elements have CSS selectors, and so are well covered for users who wish to use custom stylesheets.
One example I guess for use of an ARIA heading would be a hidden heading for a sidebar on a webpage. This might not benefit from a visual heading as would be visually distinct from the main content of the page. A hidden heading, though, would serve screenreader users well e.g. <div role="heading" aria-level"2">Secondary nav</div> (I don't know how appropriate this example be, I couldn't think of a better one though).
Do you have a specific example in mind?