I grew up in Detroit in the 80’s and I witnessed the dying gasps of the US auto industry - and I do believe that the UAW had a lot to do with killing it. The problem is, if you go back further, when they unionized, they basically had no choice - they were pushed into a corner by management like in TFA, so it was a choice of committing suicide slowly or being murdered quickly.
I grew up in a suburb of Detroit, and formed a slightly different view. What I remember is that even when there were mass layoffs, and a "for sale" sign in front of every other house on my street, there were senior auto workers putting in 60 hour weeks and collecting overtime, as was their right under the union rules.
Meanwhile, in some European countries (maybe Germany?) the unions were responding to the recession by cutting back on hours for everybody, to maintain broader employment. I remember thinking about 4 day work weeks.
The impression I formed was that the American unions were serving their narrow purpose of protecting members, especially senior members, but failing to serve as a "labor movement" with broader social goals, while taking credit for social gains of the past. It created a situation where many members of the working class believed that they were competing with the unions.