Here I created a chase from the basement to the attic. (well more than one). I use my wife's wanting to redecorate rooms to add infrastructure. (well house was two years old?) to add more chases and infrastructure. I did also find a "plumbing wall" that goes from the basement to the attic which I used.
Example: I wired one room with networking, security stuff, touchscreens and in wall speakers while concurrently redoing the room (everything really, walls, carpeting, windows, et al). This was high on the WAF and I got my stuff done.
The wiring closet under the stairs is a great idea.
The reason I mentioned what is on the other side of the wall was that I did similiar to you with one chase.
I did cut out a larger access panel (well its spread out to two studs wide and maybe 2 feet high and finished it such that it looks nice but is easy to remove for any future cabling needs. Today though there is a large book shelf in front of one access panel.