Good catch, sometimes things can be so obvious that they're easy to overlook!
While I'd agree that better tools (debuggers, and console.log) exist for debugging, the built-in dialogs do have their uses and I think it's a bit unnecessary to suggest forgetting about them. I haven't been able to find any source online to suggest they've been deprecated, or relegated to 'debugging use only' as you often suggest - perhaps you could provide a reference for this claim?
Certainly the Mozilla Developer Network (MDN) makes no mention of this in the entries for those functions. I've got a copy of Professional JavasScript for Web Developers (3rd Ed) by Nicholas C. Zakas handy, so I thought I'd see what he has to say about them:
Obviously they have their disadvantages (you can't style them), but they do have their uses within simple web apps for example. They're even in use here on the SitePoint Forums, to give a notification of privates messages and to add URLs to posts, among other things.