I have always believed , (maybe wrongly), that the role of Management Representative was exactly what it says, a 'representative of management'. So we ask who are we a representative to, and why.
It is not just within the company. If management sends a 'representative' to deal with a customer issue, then it implies that the representative has the authority to make decisions, and negotiate, on behalf of management. Same is true for a vendor issue. These things can be attended to by the QAM, but he is not the 'official' representative of management unless he is so designated, (as MR).
I have been at many meetings where the customer proposed solutions only to find that I had to carry the options back to management for approval, so then what is the point? Too many MR's are in this position, and it argues against nominating the janitor as MR, as he also just becomes a message bearer, not an active part of the system.
If the role of MR was to simply be a 'single point of contact', then it should be called "Management Contact", not representative.
To your other point, I am not familiar with 18001, but it seems they are asking for a top management position, not just anyone.