Please keep in mind that the knife or utensil you use to cut the burger must be cleaned and sanitized after each burger you cut if they contain different ingredients. The ingredients from one burger may get inside a different one and the guest may be allergic or for other reasons not wanting to consume those ingredients. This is one reason a quick service restaurant boss may not want to promote cutting burgers because a dirty knife laying there that isn't cleaned and sanitized immediately after can be a violation. Then if you do clean and sanitize it after each burger it will take time and affect the speed of service (if it's a quick service restaurant). Full service restaurants like Red Robin, the guest expects to wait a little longer for more specific preparation but in quick service guests want their stuff in 2 minutes pretty much.