It's a better story telling - establish the world where you are telling the story. And I dont mean disclaimer message, I mean a story telling element that's missing.
Hm, I am not sure we are discussing the same things actually. The in-Matrix world is clearly not governed by cause-and-effect. It not only has "magic" it literally only has magic.
What I meant above is that the so-called "real" world as shown in the movie also has magic. And that part has not been clearly established in the movie, we were just thrown that into our faces in Matrix 2, I believe.
In Matrix 1, we got the common sci fi-y tropes, like anti gravity engines, EMP, head chips, hacker green screens, - I personally can not pin point an instance where I'd say - ah yep, magic is totally real.
Am I missing something obvious?
I think I like them both actually for different reasons. (re)watched first one back to back with the new one.
What you describe could have been an interesting movie as well, but it doesnt appear that this is what have been made. Characters never doubt the reality of the "real" world. 
