They can change prices and/or update the menu at any time and they avoid printing, storing, handing out, collecting, and cleaning the physical menus.

An appliance menu server would cost practically nothing if they're already offering Wi-Fi or use electronic POS/ordering systems.

No, you can use your cellular connection all you want. It'll just eat your data. If you want to trade a little effort for a little data saving, that option is open to you.