Try as I might I cannot trace any paper that has studied , as its principle theme, the role of the toes of the human foot in interacting with the ground to provide traction (in the sense of grip ) . It does not seem possible that this has never been studied before but , as far as I am aware , that is the case . The role of toes in propulsion , particularly with regard to their length , yes . Spreading the toes during swimming to improve traction in water , yes . But traction (grip ) on land , no .
So if the role of the toes in helping to provide traction in the unshod condition has never been properly looked at before , does that mean it doesn't matter ,and is it even less relevant in the shod condition ?
As a starting point in attempting to answer these questions the following might be helpful .

I have found that most people greatly underestimate how much of the foot is actually taken up by their toes and 3 photographs /slides can make a big impression .

Photo 1 This is simply a photograph of the dorsal aspect of a subjects foot .

Photo 2 This shows the same foot with the toes in a curled position . Dots made with a suitable skin safe pen (eye liner pencil or such) are placed on the now easily identifiable MTFJ (explained to the audience as where the toes meet the rest of the foot similar to the knuckles of the hand ) and a photograph is taken of the foot with the dots in position .

Photo 3 This shows the foot with the toes back in the non curled position but with a line drawn across the foot and through the dots on the MTFJ (a join the dots type of thing ) . It can then be explained to an audience that the part of the foot distal to the line is toes and associated interproximal tissue . The reaction to the sequence of images is always the same . " Your kidding ,all of that is toes " ?

In the unshod condition the role of the toes to give traction (grip) is crucial .
In fact I would go so far as to say that in the unshod condition, toes were as important to our ancestors as flight feathers are to bird or a tail fin is to a fish . Regardless of how powerful an animal is ,or the medium through which it moves, the end point of muscular effort must be force delivered through a structure which provides good traction ( in the senses of grip ) between the animal and the medium.
Along this theme , when you walk barefoot on a sandy beach ( provided of course its safe for you to do so ) you feel your toes splaying apart as you walk improving traction ,pressure distribution and function . I believe that this type of activity ,even if undertaken only at a walking pace whilst out with the dog , might be of benefit .
So where does footwear come into this ? As follows .

If I were an experimental biologist/podiatrist/anthropologist (which I am not ) with a keen interest in the foot I would feel compelled to link the structure of the forefoot with one of its primary roles ,traction .

Also , if I were a manufacturer of glove like footwear (which I am not ) I would see that a minimal shoe which allows the toes to spread out when walking on cold wet sand but still allows the foot to stay warm and protected from injury ,would give me a unique selling point . I would , therefore , fund the experimental biologist to see if moving on a sandy substrate , wearing my glove like footwear , might improve foot health .

The experimental biologist /podiatrist , might start his/her research by looking at a comparison between the forefeet of unshod beach and shod indoor , volleyball players.

Any thoughts ?

Gerry