Besides all of the things that APE mentioned, consider the equipment needed. Each craft has specialized tools.
Audio post itself is divided up into specialties - dialog editors, ADR recordists & editors, Foley artists, Foley recordists & editors, sound effects field teams, sound effects editors, music editors and rerecording mixers. Each of those crafts require very specific equipment.
About the only things that composers and all of those audio post specialties have in common are really nice speakers and an isolated, treated room; and most indie composers don't even have the room!
At the highest levels a Foley team will have a small warehouse of Foley props. The Foley team will also have a fairly large specialized room with a projection system and Foley "pits" that have various surfaces.
Dialog and ADR editors will use specialized software, as will sound effects editors. The sound effects field team will have a lot of field recording gear, and much of it will not be part of the kit used by a production sound crew. And rerecording mixers have highly specialized rooms.
How many composers will have all that?
Now, I may be "only" an audio post generalist, but I have software that specifically applies to dialog editing and ADR. I have a separate room to record ADR, Foley and sound effects. I have a basic field recording kit and a decent mic collection. I have a large wall, a closet and a piece of my garage dedicated to Foley props (and I'm starting to run out of storage space.). I may not have Foley pits, but I have cobbled together what I need to cover a wide variety of surfaces. I have a large collection of commercial sound effects libraries and a constantly growing personal sound effects library. (A composer will collect musical instrument libraries, not sound effects libraries.) My niche is the low/no/mini/micro budget filmmaker, and I am equipped and experienced to handle that specific clientele.
And, not to denigrate composers, but their focus is and they will put the majority of their efforts into the score, not the audio post.