What is Menu and Cost?
Every dish on a menu has two prices, really. There's the one printed for the customer, and there's the one nobody sees what it costs the kitchen to actually make it. That gap between the two is what people are talking about when they say "menu and cost."
Flavor gets a dish onto the menu. It doesn't necessarily keep it there. A dish can be the thing everyone orders and still be quietly losing the restaurant money if the ingredients cost too much relative to what's charged. So owners end up balancing two things that don't always agree what customers want to eat, and what the kitchen can realistically afford to put in front of them.
A lot of restaurants handle this through what's called menu engineering, basically going through sales numbers next to cost numbers, dish by dish, and figuring out what earns its spot. Some items stick around because they're profitable. Others stick around because they get people through the door, even if they're not making much money.
The menu and its cost aren't really separate things. One shapes the other, starting from the day a recipe gets written down to the day a number gets printed next to it.