Is there any reason we should not place the monitor speakers directly to the side of our ears (such as wearing a pair of headphones) during mixing ..as is depicted in the pic.. ?

I place my speakers at this position sometimes to make space. Got curious, sat in the middle to test the sound. The stereo field is quite nice.

The main issue I can see is it turns you in to a piggy bank.
 
:D
 
In general the issue would be that most people don't listen like that so your mix might sound odd. Also it is likely to leave a gap in the center of the stereo field because it is so wide.
 
However if you like it, it doesn't hurt anything.

I think we've evolved to use our ears to best observe what's we're looking at in front of us. Headphones have got it wrong IMO.
 
Sven

I would be concerned about phase issues related to reflections off the opposite cabinet face. I think they used to call that Texas headphones.

Sycraft
The main issue I can see is it turns you in to a piggy bank.
 
:D
 

Lol !
 
The experiment came up since I've place my monitors on the movable side tables and change the angle depends how far away I sit (refer to profile pic). I would be concerned with phase issues too when the monitors are facing each other, but that is just for testing out. Normally I'll place them at about 45 degree and further apart.

The standard from a production standpoint is 60 degrees, it is what mastering engineers use, it is what studios should use but frequently don't because they don't know any better, but best to stick with that.  You may hear good separation with monitors placed like that, but you will not hear an accurate and repeatable stereo field from anyone else's standpoint.  

And you'll need a bigger Piggy Bank if you have any hardware GAS symptoms. 
I'm in a corner right now so my monitors are almost like that. I guess it's not great but I'm so used to it after 4 years it certainly works for me. I need to update my picture, that's my Tascam interface and only one monitor. 
 

I would think you'd have one big center hole w/ that set up.

Are you referring to the OP's set up or mine?  I think the OP's set up would be a little weird to work with, but my halfway there set up does seem to be OK for me. The stereo field is right on if I sit in the halfway spot. As I said, in theory it's wrong, But then you sort of get used to it and it works fine. I've certainly been cranking out mixes I'm happy with over and over for about 5 years this way now. In a way it has put the speakers closer to my ears than if they where in a traditional set up. 

SvenArne
I think we've evolved to use our ears to best observe what's we're looking at in front of us. Headphones have got it wrong IMO.
 
Sven

Agreed. Remember that the mixes we hear in headphones were originally mixed on speakers, not headphones. 
 
I suspect that setting speakers up that way would still be better than the traditional way if the "proper" setup meant sticking them right up against a wall. Getting as much air around the speakers as possible is more important than their angle.