Maybe if the Big Three had designed cars people actually wanted to buy, history would have been different.
No, but the fact that there are no unionized companies in the U.S. that are world leaders in their market segment wiggles its eyes suggestively at the idea that the problem might have something to do with unionization.
I don't view Boeing and Airbus as shining examples of success. Both get large government subsidies. Both have had their share of problems over the years, perhaps more Airbus lately. And there are just 2 of them. It's not a competitive industry. When you're splitting oligopoly profits, there is more room for unions. This actually is also the instance where I do think unions have the most standing. If there's no place else to go work, you kind of need a union. In addition to "the only mine in town" I think this also applies to fire and police departments. I don't think it applies to schools - I'd much rather see more choices (charters, etc) - but that's a much longer post.
Furthermore, nobody here knows what qualifies as a world leading company to you. That's your opinion. General Electric, UPS, all of America's major professional sports teams, Safeway, Budweiser, Coors Brewing Company, Carhartt, are unionised. You don't consider Boeing a shining example of success because they take government subsidies. But that's really besides the point because they make great planes for countries all across the world where they do have to compete. They're a world leader. Non-unionised companies have to compete with companies that are unionised when it comes to a worker's pay and benefits to get the best workers.
But like I said before, the premise of your question is ridiculous.
They're not crippled because they're unionized, they're non-union because highly skilled workers are in short supply.
When our "everyone should learn to code" and "if you're not a STEM major you don't deserve to exist" initiatives gain more traction and Google/Apple/Facebook are drowning in highly qualified candidates, that could easily turn around.
Plus, it's not like the Japanese auto-workers at the companies that are Detroit's lunch weren't unionized. Wasn't the fall of the American auto industry because of competition and market forces instead of big bad unions?