Incompetence – manager vs team

I'm in a difficult situation where I supervise several teams. Some of them works fine but some have issues.

You can divide it into 4 categories:

I = Incompetent C = Competen

1. (I) team & (I) manager
2. (I) team & (C) manager
3. (C) team & (I) manager
4. (C) team & (C) manager

I see things can work only in 4th case.

For cases 1, 2 and 3 the outcome/productivity varies. Sometimes there's blame game, sometimes covering each others, etc.

I can easily imagine situation (case 2) where manager claims that his team is below par, thus justifying misdelivery (e.g. new good manager that got assigned a team of mediocre devs). I can also imagine situation (case 3) where team has great devs, but higher management suddenly assigned them new poor manager. (I'll skip explaining case 1).

For case 2: manager should grow its team. That's theory. It will probably take 1-3 years to grow someone who has big gaps in knowledge (while higher management expects results next quarter).

For case 3: team should report poor manager to higher management. It's also unlikely as team is afraid to be fired, as manger (even if incompetent) is "higher" in hierarchy.

When I Google this topic I only find results how bad the bad managers can be. I've never seen any article covering opposite scenario – as if the world has only competent individual contributors and only skills of managers vary (I agree, there are terrible managers, and I had few, but I also experienced bad teams).

How would you deal with scenario 2 and 3 (and maybe scenario 1 too) if you were the director of the department? How to spot who's really weak vs who just blame others to save his/her job?

(So far I trust my inner guts but I'm looking for opinions in that matter)