The short foot exercise is often advocated as a treatment for flatfoot or overpronation.
It is carried out by shortening the distance between the heel and the base of the hallux by sliding the forefoot posteriorly along the ground. This is claimed to strengthen the intrinsic muscles, specifically the abductor hallucis muscle.
It is typically more widely recommended by those with a more limited or superficial understanding of foot function and biomechanics. While it is effective at strengthening the abductor hallucis muscle and a stronger muscle is probably better than a weaker muscle, its efficacy for treating flat foot or overpronation is going to be limited to those cases where a weakness of the muscle is the problem. It is not a common cause of overpronation or flat feet. There are multiple causes of this, such a forefoot varus where even those with a limited understanding of what forefoot varus is will easily see that no amount of muscle strengthening is going to fix that. There are many other causes of a lowering of the medial longitudinal arch, most of which will not be affected by the strength of the abductor hallucis muscle or the short foot exercise.
The short foot exercise is probably also going to be useful to help manage plantar fasciitis as a weakness of these muscles have been identified in those with it. It is not clear if the weakness is related to the cause of plantar fasciitis or if the weakness is caused by the limited function from the symptoms of the plantar fasciitis. Which ever one it is, it is still probably helpful to use the exercise as part of the rehabilitation.
There is nothing inherently wrong with the short foot exercise. It has its uses. It is just not the panacea that all the rhetoric and propaganda from some think it is.