Not sure if this truly answers your question, but I'll give an answer from a Taekwondo point of view.
In our kata (we call them poomsae, hyung, or tul), we were once taught to use ball of foot. And when we sparred, we did the same. In self-defense context, we assume we don't have complete mobility with the ankle, such as the case when wearing boots for example. So we learn in self-defense to kick with ball of foot (or even toes, depending on the rare application). In sport, we kicked with the ball of toes to get around the guard.
Nowadays, while it ultimately depends on the school, Taekwondo-in can choose ball of foot or instep as they deem. In WT poomsae competition and in Kukkiwon grading, we are given the leeway to choose, so long as we are consistent. Don't use ball of foot in one technique, then change to instep in another. In poomsae, we never kick with shin, because we never strike a target, so this is moot. But in sparring competition, kickers almost universally use the instep for two very practical reasons. In WT competition, they never use the shin, because that would be an illegal technique (only the part of the foot below the ankle is a valid striking weapon). Using the shin, if accidental, will go unnoticed. Deliberately or repeatedly using the shin or knee will garner a warning for use of an illegal technique.
As to the two reasons, the first is range: you are given a few free inches of distance. In competition, you generally need not worry about damage to the instep, because (1) the foot is protected; (2), you want to score points, not KO's; and (3) your opponent also has padded protection (but only on the hands, head, and trunk; not the legs or arms, and while these are illegal striking weapons, accidents can and do occur.)
The second reason has to do with electronic scoring - the sensors in the padding. In the "old" days (even as recently as Rio Olympics), the chest protectors had known bare spots - places where you could strike but there were no sensors, or the sensors didn't read well. Using the instep gives more surface area to contact more sensors, thereby gaining advantage when these sensors were not present or malfunctioning because there would be a chance of a nearby sensor that could pick up on the strike. The sensor thing was not a game-changer for those fighters choosing to use ball of foot; most (if not all) had been using insteps for years. But the sensor issues definitely placed more nails in the ball-of-toe's coffin.
You may note that throwing the round kick feels differently between the two options. With the ball of toes, you have less distance (the radius of the kick goes from the knee to ankle) and so you may find you turn faster. With the instep, the length of radius is slightly longer, thereby potentially slowing the kick ever so slightly. Also, the muscles needed to pull the toes back (ball-of-toes) are different than the muscles necessary to push them forward (instep), and that has effect on the rest of the leg's coordination of the kick.
I've discovered that kickers who are used to kicking with ball-of-toes tend to adapt well to instep, but the same could not be said of kickers used to instep and try to use ball of toes. This has effect on breaking. For one or two boards, I'll easily use an instep. For more than that, I'll defer to the ball-of-toe. But others cringe at breaking even the measliest 1/4" boards with insteps (despite sparring with instep) and completely bungle the break because of balance when they defer to ball of toes. I don't understand why, it's just what I observe.
I offer a guess, even if probably not related to your question (feel free to call me out on it! lol)
To use the instep, the gastrocnemius and soleus muscles (ie, the calf) must contract.
To use the ball of toes, the anterior tibialis muscle (ie, the instep) must contract.
Larger muscles tend to be more easily contracted than small muscles, so in this case, it takes more work (and skill?) to effectively use the ball of toe than it does the instep. Perhaps not surprisingly, when neither muscle is contracted, the foot will tend to flop, as anyone who watches young children try to throw a roundhouse will attest is very common. And in this case, the foot's instep will naturally open (perhaps also aided by the circular movement of the shin and centrifugal force?) the instep is the result, however unintended.
I doubt any of this was factored into the use of either method, though maybe it explains why some people choose instep over ball-of-toe when given a choice.