> index.pdf won't tend to play nicely with screen readers

The horrible Wix sites most restaurants end up using are likely less accessible than a PDF. The Adobe PDF reader can reflow text.

> also sucks for people on crappy mobile networks

The average wysiwyg site builder produces bundles that are an order of magnitude larger than a PDF menu. Also, the PDF is easier to cache correctly and can be easily saved for offline access.

But you can easily serve a desktop version or a small screen version.