Long subject but the quickie answer is reduced reflections and better bass.
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Diagonal placement geometrically eliminates early sidewall reflections, which imo is highly desirable. And assuming the room isn't overdamped, the energy which normally would have been in those early reflections survives to become beneficial later reflections.
In a square room, I'd suggest setting up not exactly along the diagonal, but rather rotated a few degrees. This way the woofers will each be a different distance from the room boundaries in the horizontal plane, which should improve the in-room bass smoothness a bit.
One big reason is the enhanced depth of the soundstage.
As mentioned the reduction of early reflections is probably the biggest reason.
With Roger Sanders Flat faced direct radiating electrostats ( Still the best sound I have ever
heard) he explains that the more asymmetrically placed you set his speakers up,
the better they sound. Ask him if you're a doubter.
I have two larger box speakers in a 14 x 16 room open on opposite ends to other spaces.
I tried the four different "Standard" configurations that one would use. The best was the one
with the an open space behind me.
Then I thought -WTF, let's see about a diagonal setup. Yes it was much improved that way.
Get some help before moving all that heavy gear around!!!
I use this setup in my listening room. Did it mostly for interior design benefits given my furniture, windows, fireplace, but things sound spacious and echo free. https://systems.audiogon.com/systems/9074
I think my current listening space in my hexagonal shaped bedroom has pretty much the same effect as the setup in the Vinnie Rossi article. I chose to treat the 1st order reflection coming from a short wall next to my left speaker, but otherwise the room seems to naturally sound great. Compared to the square or rectangular rooms that I've previously had, this room sounds exceptionally quiet. I can that tell there are few if any stray reverberations mainly because I don't hear the echoes that I just unconsciously thought were present in all rooms.
Echoing Redwood set up a pair of Celestion 600s that way in living room 30 years ago looking to save space and accidentally discovered the added benefits of clearer and cleaner sound on the whole. Speakers in rectangular rooms sounded muddy even when separated from all walls so I would assume the mid bass was tamed in this configuration avoiding sidewall reflections. Soundstage depth also benefitted.
It goes against the grain - yet: I have actually heard this once. It seemed absolutely fine. There is tons of great advice on speaker placement - I think all of it is well meaning and useful. My humble two cents* just keep fiddling and experimenting!
* hoping you don't have heavy and spiked speakers!
Roger Sanders specifically prefers to set up his speakers this way because of the way first reflections are aimed away from the listening position. He is quite a character. For those who do not know him, he designed the curved panel for Martin Login. After deciding that was a silly idea he left and started his own company. His model 10 is quite a speaker but like my Acoustats very selfish. When you are in the groove They are quite a ride.
The main problem with this approach other than décor are that it requires a large room. In smaller rooms the listening position is pushed up against the opposite side wall were you most definitely do not want to be.
With a short wall system if you are careful with sound absorption at all the first reflection points around the speakers you will be fine above 250 Hz. It is below that is difficult. 2" thick absorptive materials only work above 250 Hz. Multiple subwoofers help but you still have between 250 and 80 Hz to contend with. My own solution is to use line source speakers that do not blast sound all over the room. I'm sure there are others that I have not looked into. I also designed my house with a media room that essentially has no back wall or rather a very scrambled one.
If you have the room to do a corner system by all means try it. You just want to keep the listening position at least four feet off the opposite wall. The farther the better.
For those dismayed by the disjointed "look" of this setup, you could put an entertainment center type shelving unit diagonally in the corner. It would create a false wall at the 45 deg angle, but would be symmetrical with the speakers. Sonically it would not obstruct low frequencies, and it would diffuse upper frequencies. ALSO... since the corner behind the shelves would be unusable dead space, you could put a large corner bass trap there. This would be a great solution for a large room, where you wouldn't mind losing a few square feet to the corner.
In my space, the diagonal allows for good symmetry when it comes to space from walls and listening chair distance. This allows for good soundstage balance (a very important factor for me). And the space that would be needed to set the room up asymmetrically in the room (far enough away from the side walls with a large open space on the other side) would be significantly more than a corner set up.
I haven’t had my system set up in a rectangular room in years and I can’t remember the difference. But here seems to be minimal smearing from side walls in my set up. I found that there was a much larger amount of interference from the speakers sitting too close together rather than too close to the side or front walls.
So I suppose my sense of the benefit would be physical symmetry and use of space.