If you need medical treatment, will you go to a doctor operating out of an office, or a doctor operating out of their own garage? Theoretically, either one could be good or bad at medicine, but in practice, professionalism is a useful signal.
An ugly AI-generated menu shows a naive disregard for the actual experience of your customers. This attitude will bleed into the food quality.
> Every dollar spent on design is a dollar that is not going to the quality of my food.
Then throw something together in MS Word. That's free. It's not bad for something to be low-effort; it just needs to be commensurately simple.