While it is not something common, it just happens.
In Australia the food culture is you can customize almost anything on the menu and customers expect to be able to pretty much choose whatever combination they want as long as you have the ingredient and they can pay for it.
In France, a menu may not contain something you can eat, but some restaurants will create a full dish for you on the spot. It's very common restaurants with a Michelin star for example: as a veggie and foodie, I get regularly this treatment since french cuisine is very centered on meat. Some restaurants have the menu changing every day (I ate in one this week) depending of the farmer's market. The waiter just let you what's available. I know of at least one restaurant with no menu: you express a theme, and the chief will try to invent something matching it.
In Thailand, there was a restaurant were I used to go that had a regular menu for tourists with high margin meals, and a secret menu for regular customers that was actually good.
In Mali and Argentina, some restaurant menus are fake. You can't order most items, while there are items that you can get pretty much everywhere (riz au gras, pollo a la milanesca) even if it's not in there.
Now, it's tempting to decide that one path is optimum and shape society to only provide it. However, you kill diversity, margin of security, innovation, charm, and so on.
Don't get me wrong. Making the happy path the easiest and proffered way is OK. Offering a digital menu and payment system as a main option is great.
But making alternatives close to impossible is, at best, a good way to end up with with a bland life, and at worse, will create a dangerously inflexible and intolerant system.
It's why we should keep cash, paper forms and phone support despite the automated main experience been more efficient when all goes well.