You seem to not be taking into consideration:

• lag
• extra information required for graphics stuff, like shadows

The reason your client computer needs to know the opponent's location when they are still 1m on the other side of the wall, is because, within the next 100ms, you might make a jump+move action which lets you see their shadow or the tip of their weapon.

The shadows and reflections need to be calculated on your system or the server would be doing too much work and if you find the opponent pop up where they clearly were not, 50ms ago (because the server just told you now), you won't be particularly happy either (I know I won't).