There's simply no strategic advantage in firing him now. Of course, given the way the Chargers seemed to lay down last night, Staley virtually guaranteed he'd have some time to catch up on his Christmas shopping.
A lame duck coach may not have the same interests as the organization. He knows he's about done and will want to put himself in the best light for future employment, win a few games at all costs and not finish on a bad tailspin. The team might want to see what they have in certain players and give some playing time to guys that might not necessarily be the best for winning now. Maybe the team can direct an interim coach how they want to develop players better than they can with an established coach.
If the coach has lost the team, which last night somewhat indicates, there's no point in him staying around. When it gets to the point where you want to fire the coach the future is now the goal, and if he's lost the team that can't be ideal for development.
You can't interview coaches that currently have jobs, but you can start informally talking to agents. That's a little bit more awkward when a guy still has the job. You could probably start talking to college guys, see if Jim Harbaugh is fed up with college rules
It probably doesn't matter that much either way though. I say if you think he lost the team and you know you'll fire him end of year regardless, then it's time to make a change.
Firing the GM is also a bit odd, but I guess not a lot of personnel stuff is happening at this point before the end of year.