The largest issue is that you have to re-create them every time you make a change. You have to create an entire new image, and update the coordinates for the map, which is arduous. They are also not very mobile-friendly, tend to waste a lot of bandwidth on the filler space, and you are somewhat limited in what you can do with the link shapes. It's much more efficient and cleaner to create the elements separately so you can easily update them, and they can scale better. Also, SEO as the other responder mentioned.

Accessibility (probably not so great on a screen-reader,) and SEO (not a proper link with content), I think. Of course, there may be other reasons, too.

Accessibility was always a concern, and mobile is probably now another one. You'd have to recreate the image for mobile screens, re-map it...