Mayo and cheese might be skipped if the person is trying to be more vegetarian. I've always found mayo to be unnecessary and kind of gross on burgers anyway. It's only useful if your meat is lousy or you've overcooked it really badly.
Many high-quality burgers have mayo by default. Au cheval/small cheval come to mind. Mayo is useful for adding flavors, and can protect the lower bun from water-based liquid penetration that would weaken the structural integrity.
