I agree, but that’s still manipulative. “Get mad at me, with whom you have no recourse whatsoever, rather than considering whether anyone else might have contributed that you could possibly effect.”

Wouldn't adding that to the statement have the same effect but also be honest? Perhaps the effect would be even greater given that people wouldn't feel like the need to guess at the real reason?

I guess it's better than some approaches such as "we can do better."

Shouldn't that part be obvious? "I take full responsibility" means you should blame me and only me. That's the very definition of responsibility.

You could see it that way, I guess. To me there's more requirements to taking responsibility than to just claiming such, especially dishonestly. Some quick research suggests my interpretation isn't solely my own.