There's a good book (albeit, a bit repetitive as you read it) about the fall of of GE. If I remember correctly the book basically confirms what you said about Immelt inheriting a lot of problems that were hidden behind accounting complexity at GE.

https://www.amazon.com/Lights-Out-Delusion-General-Electric/...

Not that Immelt was a star either, but he he wasn't the person who created a lot of these problems.

Not quite what you're looking for, but this book is an intriguing description of the struggles of Jeff Immelt and later GE execs to keep up GE's success after Welch's departure. In particular, trying to manage GE Finance: https://www.amazon.com/Lights-Out-Delusion-General-Electric/...