Largely because he's been dealing with similar questions for years, I imagine.
If you want to have both AotR and ICW installed at the same time, it is doable, but requires you to maintain two corruption/data folders - one modified by the AotR installer, one that wasn't. Here's a step by step:
1) Start with a clean install of EaW+FoC.
2) Go into the corruption folder, make a backup copy of the Data folder - call this "Backup data" for now (don't actually use quotation marks, I'm just using them for clarity).
3) Install AotR through its installer.
4) Rename your current data folder "AotR data".
5) Rename "Backup data" to "data".
At this point, your game is set to use the vanilla data folder, and will be compatible with ICW or most other mods. If you want to play AotR from this point:
1) Rename "data" to "backup data"
2) Rename "AotR data" to "data"
To get it back to vanilla or ICW compatible:
1) Rename "data" to "AotR data"
2) Rename "backup data" to "data"
Hopefully you can see how this works. You'll need to swap the folder names every time you decide to change which mod you are playing - if you get them mixed up, a little trial and error with starting the game will figure out which folder is supposed to be which, but it's annoying to do this so try not to get them confused.