Why meatgrinders are terrible for creating backstory

[Mechalich]

So anyhow, I'd say the underlying question that's more salient is, is it better for the thing that binds characters together to be something that existed before play, something ongoing during play, or something created during play but quickly resolved?

Well it depends. One key question is whether or not the group was deliberately assembled for some objective - ex. a group of special forces soldiers put together by a ranking officer for a series of missions - or the group formed more or less organically and now finds itself forced to pursue whatever objectives the campaign has - ex. a vampire coterie suddenly facing a major crisis in their city.

In the former case, the binding factor is ongoing, the PCs are all members of some organization and they are expected to fulfill that organization's wishes (willingly or otherwise). It can be resolved quickly, if the campaign is uninterested internal organization tension, or it could be a source of ongoing plots if the campaign wishes to go down that road (consider how in some police procedurals the main team gets along fine with their superiors and focuses on solving crimes and in others departmental politics are a far greater source of impediments than anything the criminals do).

In the latter case, it's much better if the group resolved why it exists before play, because there's not going to be anything in the campaign that fosters ingroup solidarity and there may not be any actual in-game reason why the characters can't just say 'screw it, I'm out' and have their PCs leave, especially since it might be entirely in-character for them to just do that (especially since the reason people don't spontaneously quit their jobs a lot in the real world - money - may not be operating as a constraint in the fictional one).

And forcing a backstory on somebody who doesn't want one just doesn't work.

Some games demand at least a modicum of backstory. D&D is unusual in that it tends to take place in a vacuum. A PC can just be some guy who wandered into town heavily armed and why that happened isn't particularly relevant while you're delving through the ruins outside of town. However, many other systems and settings have significantly higher demands. In particular a setting that either imposes inherent traits upon a character - ex. you're character is a vampire, how you became one is a question that requires an answer - or has universal historical events that touched literally everyone in the setting - ex. in Eclipse Phase the hard takeoff rendered Earth uninhabitable during your characters lifetime, and you can't not have a 'what happened to you during the Fall?' for any PC.