Brad Childress is a long time Reid assistant and a former HC. Last year, he was with the Chiefs as a special assistant. This year, he was named co-OC. He has the clout, the experience, and, likely, the desire for more than that. He's only 60.
It is highly likely that he has been with Reid these last few years to groom Nagy for the OC position. I have a hard time believing that Reid would block him from a job that gives him more responsibility and status, provided Childress wants the job.