The way I read the US constitution, every federal government agency is necessarily contained in one of the three branches, since the entire federal government is made of and only of those three branches. FCC is not in the legislative branch -- constitution is clear that that is only the congress, it is not judicial -- the constitution is clear that those are the courts. So it is in the executive, which makes sense since its job is to enforce law -- the job of the executive branch. The executive branch reports directly to and is directly answerable to the head of the executive -- the president.

The congress cannot legislate a fourth branch even if they wanted to. They'd need a constitutional amendment for that. We have thus, by a simple application of reading and logic concluded that this is precisely as is expected given the US constitution.