I think staff should be fine to have characters in any game, even a plotting one. I think on a practical level it’s not a good idea for the staff character to be taking the lead in a story plot they’re running, if only because in my experience it’s really hard to both GM and actually meaningfully pilot a PC! I’m sure it can be done, but I think it’s hard to do well. ime it’s much more likely for it to be ‘and staffpc was also there in the background’ than ‘this was actually the staffpc show’ but I am not surprised by the existence of the second.
In the hands of a conscientious gamerunner, i think a staff PC is another tool to help build game wide engagement. I think there’s a lot of little things those characters could do to encourage plot involvement that are hard to do with NPCs. A staff PC can “just run into” someone to organically bring them into a plot in a way that more formal NPC involvement could make favoritism, for example. “Passing along” IC gossip from other PCs is honestly a really important function in games so having a character on the ground to do that now and then is probably nice. Though I’m thinking of smaller games where it makes sense for everyone in it to be able to talk to each other.