Caro is often highly critical of LBJ. He is the foremost expert on the topic and has spent decades researching his books. If there is any "myth" in this context it is JFK's "Camelot." JFK accomplished very little. Certainly nothing of importance with Civil Rights. Rather than the shining prince of white liberal elitist lore, JFK was an entitled lightweight with a well documented record of adultery, drug use, and undisclosed serious medical condition that he lied to the public about while running for office. More Harvey Weinstein than King Arthur.
Caro says he "detests" and "loathes" LBJ for his appalling behavior and dishonesty. And he documents much of this behavior in his earlier volumes; the horrible mistreatment of "Bird", the dishonesty (LBJ's fellow college friends called him "Lying Lyndon") and more. In fact, Caro says that the LBJ family stopped responding to his requests for interviews because they were angry at his portrayal of LBJ.
My guess is that his next book will document the duplicity and corruption of LBJ during the Vietnam War. Anyone who thinks Caro is mythologizing LBJ hasn't read his books.
LBJ's a difficult man to understand. He was so awful, so mean spirited and deceitful. How could someone like that be so right when it came to civil rights and racial justice? People need to say "He was awful" and all of his work for civil rights was for personal gain. And nothing more. But that's simply not true. Caro shows this. So does Dallek, So do other historians.
People can reject all of this documentation if they want to. Or need to.
As for your JFK comments: in his defense he always was dealing with crises; the historian Richard Reeves called it a "crisis Presidency". Some were his fault, some beyond his control. So he really had little time to deal with his domestic agenda, either civil rights or Medicare or the tax cuts. And it took someone like an LBJ, who knew how to get legislation around the various "fiefdoms" that powerful Congressman held, to push it through.