overgeeked
Open-World Sandbox
To hopefully make this make sense, think of the game as an anthology, either a big book of short fiction or an anthology TV series like Twilight Zone. The important bit is there are various writers, an editor, and that all the stuff should at least roughly conform to a given theme, like say this anthology is about ghost stories...while that anthology is about time travel...and that other one is comic fantasy.Sure. You think the GM should be the only source of story. Any player "contributions" are to be vetted, manipulated, and approved by the GM before being allowed into play. Effectively, player "contributions" are just writing oromots for the GM. Hence your focus on backstory as a GM approved set of GM prompts for GM provided story.
In this framework, ANY mention of the GM approving anything is subsumed into this thinking. No amount of "say yes" or "should" or any of the other changes to GM advice in 4e matters because we can just beeline back to "the GM is the unquestioned boss, okay, players only get things at the GM's desire". There can be no other explanation because of how obvious it is that the GM is just in charge.
The players are the writers. The DM is the editor. The theme is generally agreed to by everyone involved. "Let's play D&D" followed by "okay" is everyone agreeing to the theme. Roughly: we're playing fantasy adventurers in a fantasy world where magic is real and dragons exist, etc. Or whatever else the theme might be. Ravenloft, Theros, etc. Epic, low-fantasy, sword and sorcery, etc.
But, it's obviously more complicated than an anthology of prose or TV episodes...it's a single game, set in a single game world...that all has to fit together to make any sense at all. The editor picks and chooses what comes in because if they don't, then you have tonal whiplash. Time travelers in faux-Medieval Europe...but it's a fantasy game without scf-fi elements, etc.
The DM isn't the source of the fiction, the players are. The DM and/or the group sets the theme and everyone agrees to engage with it. The DM, effectively, hands the players writing prompts (situations) so the players can write the fiction (engage with the setting), i.e. creating the story of the game, then the DM has to make all the fiction the players generate work together as seamlessly as possible.
So yes, generally, you do need someone in charge of making things work together. Otherwise you have a loose, nonsensical mishmash of whatever. You can share that authority around the table, but that's not how traditional games are set up.