FAST/WAW with a rear firing tweeter?

Just sitting here thinking about the mix/mastering process and the typical use of shelf filters to add 10khz and up content to recordings which develop the sense of air and the acoustic space we’re all accustomed to. For HF drivers without a horn lens, these frequencies are very directional and if listening off axis, either are too low in amplitude or are riddled with ragged response and break up modes. But what if we used tweeter on the back?…..say crossed over very high around 7khz or so. We could trust the front wall and obstructions to splay the content back into the space, returning that sense of air and space. I’m sure there’s some designs that use this method but I’m just inquiring for those here in the DIY realm who’ve given it some thought or a try?
 
I forget who now, but long ago there was an European? 'hornie' on the HE forum that first tried a second horn, then just a driver and last a Fostex? tweeter he kept, though don't recall whether or not his being near/at a wall /corner.