There are a few old games like "Midnight Resistance" that are much more enjoyable when the joystick can rotate.... but I've never seen a single home built arcade machine that had any of those. I'll likely buy a cabinet some day rather than make it, because I'm not so good with my hands; I hope by then I could find one that does have a rotary joystick.
It's certainly not a drop-in replacement, but you're right that those kinds of games need a certain feeling.