Pizza's different because it takes 15 minutes for them to make it. It's not really a choice of going to the store to order vs using an online form. It's a choice between calling and using an online form. Calling is already fairly impersonal, and on top of that you normally end up on hold, then you have to read them your credit card number, etc. Online ordering can indeed be less hassle than calling in an order (at least after the initial hassle of setting up an account).

Let's also not forget that Square is presumably not just targeting coffee shops and restaurants with this. You can take a sweater to the register and pay with card case.

Some of the places I order, they get my stuff ready when they see me walk through the door. Much more convenient for me than having to fiddle with an ordering system even if there's a saved order I can repeat.