13th Age has a nice feature here, in that they don't describe much about the world at all but instead simply have a group of powerful figures that dominate world politics. The Diabolist, the Crusader, the Dwarven King, the Priestess, etc. are the people the system talks about. Characters don't have any more specific background than that though, so if you want to be rich or affiliated with the merchant bank of Lor'Dai or have a baron after your head the game has nothing concrete for you. The idea of a few specific people who dominate the world is cool and provides some serious structure for world building.
Another example that I don't know if I can follow but which is useful is World of Darkness. That game is set in the modern day so there are backgrounds for being really rich, for political power, for having minions, friends, or an influential mentor. However, the game is specifically supposed to take place in a particular city so it isn't easy for characters to get away from their pasts. In Heroes By Trade the world is a pseudo medieval magical setting so if everyone decides to get on a boat and head to another land there is nothing stopping them thematically or mechanically but it would mean that most of their background would suddenly vanish or be irrelevant. People can hop on a plane and find you anywhere in the modern world but that sort of thing isn't going to work the same way under the Heroes By Trade world assumptions.
I came up with a bunch of ideas to help people build backgrounds, like spending points on wealth, contacts, friends, and experience and letting them take enemies, issues, and problems to counterbalance that. Problem is, if I build that into the system then a lot of it won't make sense or come into play at all if the group decides to be a roving band of thrill seekers travelling far and wide. Your friendship with the local blacksmith's guild and the fact that the sheriff wants to find any reason to string you up is irrelevant when you are three weeks travel away past the Swamp Of Doom.
To make a background system that stays relevant I need to tightly control the world. I would have to make up a lot of the stuff that influences the lives of the characters and mechanically ensure its continuing importance. That is possible, but such control really pins the GM into a corner in terms of storytelling, and means that repeat stories feel quite odd. Every story having exactly the same set of powerful people or precisely equivalent factions just feels wrong. When I make a new campaign in a new world it is wild and woolly and very idiosyncratic. No way would I be interested in a system that required my campaign to conform to specific constraints the way 13 Age does.
Which I guess means that the very simple system I currently have in place where characters pick a couple of Assets and a couple of Problems and then work with the GM to define those things is really about my style. I like characters having some hooks, both good and bad, and I am happy to work those into whatever story or setting I have going. What I don't want is a system that manhandles their social connections and history into some fixed structure that doesn't mesh with the world I built.
So I guess what I am concluding is that I built the game I want to play, and although I can probably do some useful stuff to improve the current background structure it is the structure I intended to build... so many I should just accept that and go with it.