I feel the Big Three were crippled, not by competition but a total lack of serious competition. For decades they competed only among themselves and only to a very limited degree. Each had their own piece of a very large pie and things were good.
Car makers needed workers to build their products. With few ways [and little desire] to demonstrate superior value, higher cost would be a disadvantage. With unions, this cost could be more or less mandated on their competition. If all automakers had to pay the same labor cost, it really didn’t matter so much what that cost was. Just pass it on to the public in the form of higher prices.
The same might be said of many cost. As long as they are mandated to everyone competed with, poor management may feel there is little need to control them. Just keep raising prices and Joe Public picks up the tab. No need to increase efficiency, that would take effort. No need for a better product, we're as good as the competition.
This is a very vulnerable position. One I feel many businesses and organizations today are in. As long as the public has no alternative, it takes what it gets and pays what it cost. People do not ask for innovation, but they know it when they see it and have long memories. An efficient alternative with innovative products [services] is the death knoll for lackadaisical management.
I do not believe the demise of the Big Three began this year, nor this decade, nor in the last twenty-years. The seeds of their problems have existed for sixty years and except for artificial means (tariffs, protection, etc.) would have manifest long before now.
Jobs will be loss, not to competition but to ill management, short-term greed and lack of innovation. No man should start looking for the fire hydrant when his house is in flames. Every business should compete, everyday. Not with any perceived competitor, but with themselves to be better than the day before.