The success of a project with many contractors that are either competitors or are all hired by a GC-type owner depends upon the sophistication of the owner and the owner's field coordinators and inspectors. In the industrial sector we do this regularly. In some cases we will award multiple intertwined scopes to the same contractor because of the level of integration - for example if many cables need to be pulled in the same cable tray or if the site is extremely congested. Often we will bid the scopes of work separately and have two competing contractors working in the same process unit at the same time. Generally coordinating the electricians with the other trades is more difficult than coordinating the two electrical contractors with each other. Even if we hire a general contractor and they subcontract the electrical, the general contractors are usually not particularly knowledgeable of electrical work and have a hard time overseeing their subs, so we as an owner have to get involved.
One factor that makes some of this easier is that although we do not require union electrical contractors, the vast majority of our electrical work goes to union contractors. The electricians doing the work all know each other because we have a fairly small local hall, and all of them have worked with each other at times and worked for the other company - it is in their best interest long term to get along because they never know who might be their coworker or supervisor on the next job.