Production capacity was probably the biggest driver for having multiple plants. Each assembly plant has a certain capacity, and the demand for Mustangs outstripped the Dearborn plant capacity. Ford could have dropped other car lines or moved them to other plants, but making changes to established lines has its own problems. Adding plant capacity is not quick - it takes years to plan and build new floor space and equipment and train new workers. The labor market in a given area can limit expansion if there's an insufficient number of skilled or trainable workers in that area.
Although redundancy in multiple sites is a benefit, the headaches of trying to get multiple sites to do things the same way offset those benefits (in my opinion, based on 20+ years of dealing with that exact situation!). Ford did a damn good job building nearly identical vehicles at three plants in three distant locations. But think of how many details we see that differ slightly between Dearborn, San Jose and Metuchen. Workers, engineers, and management all tend to find ways to do things faster, better, and cheaper, and those good intentions lead to differences between sites. Up to a point it's beneficial, but once the differences in materials and techniques become too great it starts to cause problems.
In short, three sites was probably the best strategic move for FoMoCo as a company building dozens of different vehicles. Looking only at Mustang production doesn't tell the whole picture.
