There are a bunch of different reasons that not many people play Call of Duty on PC, but the most obvious ones are:
The PC port for Advanced Warfare is not the worst port I've ever seen; that goes to games such as Call of Duty Ghosts, MW3 and 2, and AC Unity. But the port isn't all that great, either. Unless you have a great PC, your game won't run well, leading to frustration and an overall worse experience. I'm lucky that I have a 770 to run this at over 60 or I wouldn't have played it as long as I did.
Most people don't want to drop 60 bucks on a game anymore. You're forced to on consoles, but on PC games are getting cheaper and cheaper through sales and the like. If you knew that the game was going to be twenty bucks off by the time Christmas rolls around, and it released in November, why would you buy/play it on launch? More importantly, digital versions of games should not be 60 dollars; it requires no packaging, manual, disk, or transport to stores, all it requires is to be hosted on a digital storefront.
3.. There are better FPS games on the PC that are all infinitely more popular (on PC)
I'm not having a go at Call of Duty, because it's fun, but it is pretty brainless. Games like Counter Strike GO (Which is only 15 bucks, or 7.50 on certain sales) and Unreal Tournament (which is completely free to play) all offer quite a lot for much less money than Call of Duty, and they come with free map updates/weapons, unlike Call of Duty which charges more.
They lied again. They said there would be dedicated servers and they flat out lied to our faces. But nobody cares enough about it to do anything about it so they're going to keep doing it.
Black Ops 1 had it, and it was one of the most popular Call of Duties on Steam besides MW2, which was a massive hit. It's a standard in most PC games, and the fact that I can't just see what people are playing and play it pisses me off to no end.