My typical client has an owner, and an office manager (quite often the owner's spouse). They have 7 production employees. Each employee is expected to perform all functions including quality and material handling.
In one case, I was brought in after a previous consultant wrote their QMS. It included the Vice President of Purchasing signing all PO's showing acceptance, and the Director of Personnel establishing and maintaining training records. That was stupid for such a small company. Unfortunately, many folks want to over control processes as if all companies had 3000 employees.
Do what makes sense for the size and type of company.