Not sure what the OP meant about "it switches the screen off / funny stat view on" as that's a FEATURE of the S4. When you cover the screen it goes off (as a PC goes to "sleep"), presumably to save battery power. As for the S-screen, the stat window shows for a little while through the S-window. If you tap the power switch without opening the case, the stats show again. If you open the case, the screen wakes up.
I just got my second case for my S4. The first one did not ever stay closed and I had to keep a rubber band around the case. Not very elegant. Now, however, this one stays closed and is not too bad looking. I'd prefer it would be leather instead of the plastic but hey-ho, until I find a leather one that is similarly designed, it'll do. I've attached a photo.