Unless its a national chain, the ones in my area are either building it from scratch or using a template. The made-from-scratch are painfully obvious in that they look like some high school student with a touch of experience cobbled it together. And that's probably what happened - the owners child or niece/nephew did it.

The template sites are obvious because the owners chose a feature-filled template with all of the bells and whistles but have no use case for all of the frills. There are empty carousels, tons of extra white space, empty link slots, and a halfway responsive mobile experience.

Considering the above, a static, zoom-able HQ image of the menu is not a bad option. It's not optimal, but it's not bad. It tells the restaurant's name, phone number, business hours (possibly), address (again possibly), plus the entire menu. That ticks all of the major boxes for information that a customer may need.

I strongly suspect it is as simple as restaurants tend to not have much money for anything that is not strictly operations related.

I think in context the parent was somewhat suggesting the opposite though. The websites for (higher-end) restaurants and hotels are often this mess of sliding images and pop-ups that can, among other things, make it almost impossible to do something simple like find the address, make a reservation, or look at the menu. And a lot of this was done in Flash at some point.

I suspect it just became a sort of arms race with everyone competing on sizzle rather than usability.

What you're describing is pretty much small businesses everywhere. Presumably this is a lot of Squarespace's target market.