This study indicates that squatting in shoes with an elevated heel activates the calf muscles (gastrocnemius) more compared to barefoot/flat shoes. This paired with the fact that it recruits more quad fibers, puts less (unnecessary) strain on lower back and Tibialis muscles made me decide to use weightlifting shoes for my strength training Instead of flat/barefoot shoes.
The differences aren’t very significant but the same minor differences are also seen in other studies that looked at the effect of heel elevated vs flat on squatting. I must say I do understand the barefoot argument because it actually feels quite nice, but I still prefer the weightlifting shoes for squats.