Actually all of the game mechanics should be stopped when the game is paused.
The most likely culprit is the graphics pipeline still being busy assembling and sending data to render to the GPU every frame, since even though the 3D world is paused, the thing has to keep on operating because of the UI.
It should be possible to make it less of a problem if the UI you're interacting in during pause is on-screen 2D and all the 3D stuff is fully static (i.e. no autonomous movements such as simulated wind on leaves or running water) but depending on the graphics pipeline implementation being used, it might be too much trouble because you need to somehow have it stop rendering the 3D stuff and only do 2D.
Also, EA being as they are, I doubt the programmers had the time to go after a "cosmetic" (lowest priority) issue that probably has system design implications.
If you truly want the game to pause, you would sit at the loading screen every time you unpaused, as you just stopped everything and it now needs to cache back in to where it was. Once it is all loaded back in, your CPU and memory loaded back up, the game can unpause. The game also has things running to prevent crashes, frame issues, memory management, etc. This is why you get a fair bit on the CPU and RAM even on the opening cinematic, it's loaded up with all that extra stuff for environment.
Obviously that's not a pause feature, rather essentially what happens when you save and then load the save.
I agree with that, though I suspect it's still running the full render pipeline in the background but I was particularly confused about why OP expected memory usage to drop