The NFL has a system to assure that good teams become bad and that bad teams can become good quickly.
Very rarely do you see good/great QBs on bad teams. Not for long. The NFL skewed the rules so far that teams with exceptional QBs enjoy a significant advantage over teams without them.
QBs are the key to success for an NFL franchise. You can almost get by with a mediocre coach and exceptional QB. You really cannot have sustained success over time even with a good coach if you haven't at least got a top-tier QB.
The only team I can think of that has a great QB that isn't winning at a high enough clip is probably the Chargers, you could also say the Texans but that was such a mess the 2nd coming of Joe Montana would have trouble winning there.
Why does this matter?
Because when you have a tremendous QB you get to win for years, until that QB becomes less effective. (Even though, though...see Green Bay)
Otherwise, you can have a good or even great coach, and a solid roster, and still not do fantastically (see the Patriots)
So we had our QB and our winning. Now teams like Buffalo, Cincy, and maybe the Chargers will get to win.
Sure, the 49ers can win without a QB but that is more an outlier than the reality.
Picking lesser QBs off the scrap heap might be able to help us, but honestly - if Bill couldn't make it work, Carroll won't be able to with the same guy. Bill is one of the greatest coaches in the history of the NFL. He runs rings around Carroll.
The more reasonable move is to shoot for a playoff slot and enjoy the wins we can get. The idea that we can just make our way back to the top of the playoff teams isn't reasonable. And I am not sure what bringing in middling QBs do except prevent you from failing enough to get a good draft pick & reload.
There is no 'patch' for this. Maybe if you are the Rams with a ridiculous roster full of stars, you can get by with a QB that is not exceptional but very good. Maybe if you are the 49ers, you can coach your way out of the mess...but not in a sustained way, with a few peaks and lots of valleys. But the likely solution is going to require a great QB. That seems more a luck thing.