So there I am, so happy to finally be finished with my house. Wait! I forgot my mailbox! Hmmmm, what's the best way to make a mailbox? With a chest! So I go, get a chest, place it down, and- dang. It looked pretty bland. I know what it's missing! The flag-thing on the side. So I stopped and thought and thought some more. A lever will do the trick! So I make my lever, walk back over to my house, through the gate, to my mailbox, and right click the chest. (Now of course I forgot to shift + click so I ended up opening the chest instead. It was pretty goofy of me.) But what's this? It...wont...go...on! (I say as I am spamming the right clicker. After a solid couple of minutes trying all these "methods" of putting levers on I finally realize- levers can't go on chests!
So here I am, on Planet Minecraft, trying to find out why the heck levers can't go on chests.

Here are a couple of reasons I believe it is not possible:

Chests aren't a whole block! It would look kind of weird having a floating lever. But then why can item frames be placed on chests, columns, and even fences?  

Since chests open and close, it would be physically impossible to have a lever on a surface that isn't even there half of the time. BUT YET MINECRAFT HAS FLOATING DIRT  . So, not sure on that one.