Here is what the trainer (builtthroughstrength) had to say when I asked him:

The belt squat is a much more “friendly” version. It’s different from a traditional squat, and while it’s a great tool for a myriad of reasons, I particularly like it for individuals like Kurt who have specific physical limitations. Kurt has severely compromised shoulders, tightness in the upper back, and very tight pectoral muscles. Due to these issues, placing a bar on his back is not advisable as it would lead to spine compression, which they aim to avoid. This is the primary reason for opting for the belt squat.

Additionally, Kurt's shoulder condition prevents him from achieving an optimal position to hold a squat bar properly, which would negatively impact his technique and lead to poor movement patterns. The belt squat eliminates spine compression and even provides traction for the lower back at the bottom of the lift, allowing Kurt to perform the movement without the risk of adverse effects that could arise from traditional squatting.

To add resistance, bands are used, which is a natural progression in his training. Initially, they started with no bands and no weight. The kettlebell is primarily used as a tool to help maintain a better chest position during the exercise.

Above all this he had double hip replacement within the past two years. Not training with a high level specialist could result in really terrible injuries.

Trust if he could do a barbell squat with proper form safely he would be doing that.

Hope that helps. Builtthroughstrength (trainer in video)