Wouldn’t the better solution just be to have an app, or web app, that users pull up on their phone? That is: why should a restaurant pay to provide the hardware that most are already carrying with them?

No.

A geek would happily install an app on their phone. To us, it would seem nifty, fun, and easy.

A regular person would walk in, find out they have to install an app on their personal phone to order lunch, then walk out and find a restaurant whose head was not up its own ass.