Now, to be absolutely clear, in case I missed it before - the mechanics don't ban you from using player created backstory elements. What the mechanics do do, though, is allow the player to "fence in" three or four things from their backstory that they don't want the DM to play with. Now, there's no reason that a player has to use any of those. He doesn't have to. It's an option, not a must.
So, if the player wants to have a mistress in every port, as an example off the top of my head, but, doesn't want this to become a "thing" in the game, he just puts that in his Background and that's the end of it. It's just a big old signpost saying, "I, Hussar, the player of this character, do not want this specific element of my background to become the focus of play".
Which, really, to me, isn't that big of a deal. Take the patrons discussion that we're having. Seems the perfect solution to me. If the player doesn't mind if the patron takes a more active role, then don't Background it. OTOH, if the player has no interest in that, then, fine, fence it in and the DM can go play with other stuff.
I'm not really sure where the resistance to this idea comes from. Seems like a perfect solution to me. If I don't want this or that part of my backstory to be the focus of play, shouldn't that be my decision, and not the DM's?