Whether or not you've read my prior piece on the short foot position, this bears repeating: the target organ/system of training is the nervous system. The nervous system coordinates the sensory inputs from the body and determines outputs thru expression of movement — whether these outputs are good or bad is determined, in part, by the type and quality of the sensory input. Barefoot training is another method where we can really access the nervous system and demand positive adaptation by challenging the many joints of the foot.
The foot is loaded with afferent nerves sending sensory information on joint position, surface changes and feel, muscle tension, etc. The high density of nerve-endings in the foot as well as their developmental importance, demands a big representation in the brain (read my post on grip training). By constraining the foot with shoes (especially those with a big drop) and socks, we deprive the foot (and brain) of valuable sensory input. When the foot is unable to feel the ground, the body doesn't know where it is in space and often demonstrates maladaptive co-contraction — too many muscles on at the wrong time. We see this in those with neuropathy but less nefariously in people with osteoarthritis and after ankle or knee injury/surgery. It's like walking on ice all the time, fixating joints with muscular contraction when you can't feel the ground.
My goal here isn't to get into the foot strike patterns associated with barefoot vs shod running (we'll save that passion for another time). However with most of our foundational strength movements, why not go barefoot? And I mean full barefoot — those feet should be straight-up sensory vacuums taking up as much sensory information as possible. The less garbled the message between the skin and the ground; the better. With loading of the bare foot we can optimize neuromuscular efficiency by activating appropriate loading responses and reflexes while cutting down excess muscle contraction. And it's hardly "dangerous".
The best athletes are able to turn ramp up muscular tension only when necessary - reducing unneeded joint loading. If optimizing recovery sounds awesome (it is), start integrating barefoot training into warm-ups and strength movements. Ever wonder why martial artists, dancers, and yogis go barefoot all the time to enhance sensory awareness, yet we strap on thick socks and shoes to do squats? Plus as a coach and therapist, watching a movement barefoot makes it way easier to monitor the ability to maintain a short foot position a key indicator of readiness for progression.
Even when performing movements that may require shoes (box jumps, sprints, etc.) going barefoot for the warm-up prep is incredibly valuable to prime the nervous system for loading. What better way to have primal output and adaptability than to have your feet fully on the ground during training - the way we evolved.