If you squat with a wide sumo stance, then you might not benefit from squat shoes. People often prefer a flat shoes like Chucks if they are using a really wide stance.
I am by no means a squat expert. I've spent years pretty much avoiding heavy squats, and I'm only recently getting back to working on my squat and am learning to front squat. I have really excellent mobility BUT now that I'm doing a lot of deep squating and OH squats with the Oly lifts, the squat shoes really help me keep my spine neutral, especially when I'm balancing a BB overhead.
The wider/ firm platform of a squat shoe is better than your narrow natural foot if you're trying to have a stable surface for deep squatting with a more standard or Oly type foot placement, IMO.
I have noticed a huge difference after trying to take Oly classes in Chucks.
I still like to DL in Chucks or barefoot.
Alan talks about squat shoes a bit at about 2:45 into the video.