As Detroit heads further into the dumps, it makes no sense for the headquarters of each company to stay in Detroit. The people that work at those locations have to live in the city as it spirals down to failure. It's unfortunate, but in the interest of the companies only, they should relocate to thriving areas that could provide better living conditions and better manufacturing employees. The image of Detroit can only be used for a positive image for so long. Eventually it's going to make them look bad for staying in the city.
From an economic stand point it makes sense for the Big 3 to leave Detroit since it is a financial disaster there. However, from a political and marketing stand point it is unwise for them to abandon the city that helped birth them. Also, it could marketed by the other two one the first one leaves as a way to show their commitment when another leaves which would endear that brand to the populous.
I'm not certain that it matters where the Big Three US auto companies are located. Detroit certainly needs what little jobs are left there, so I don't feel they should abandon it just for relocation. Factories are in different parts of the country as well. I know of at least one just north of Saint Louis.
The city of Detroit is already struggling and taking away more job's from the area is not going to help it at all. Keep them there and then recruit people to move there to work and give tax breaks to people. They economy there is not that great and places are going out of business.