It's an interesting idea and one I know I've heard discussed numerous times, even if not ever done.
The concern is usually consistency in how the characters are played. Even with notes or bullet point personalities or w/e you give them, there is always going to be a lot of variance in how they're played.
Certain players will interpret certain descriptors differently, players will emphasize specific traits over ones that other players emphasized, some players will be too 'nice' if they're running something for their friends, and because of all that sometimes there will be significant differences in how those characters interact with pcs in different plots/etc.
How do you combat that? Staff has to read all the logs? Idk!
ETA: you can already kind of see this in comic games, when different people run plots with the same villain/etc