I do think if a man/woman finds that INCREDIBLE person, the person they don't want to let go, I don't think they would be okay knowing that the person is out and about with every Tom, Dick, and Harry.
And see, there the ridiculous notion of relationships = ownership comes in to play. You do not possess the people you are in a relationship with, even if they are your best relationship ever and you never intend to leave them.
A person is not a prize to be won and kept. They are not a toy that you don't allow others to play with.
Ownership in a relationship is an active, voluntary consensual agreement that should be made with the deepest of consideration and clearly defined boundaries. It should NEVER be the default, or taken as part of the dating or marriage package without consideration.