For Soldiers, or really anyone on the street dealing with shoes and high friction surfaces, I emphasize actually moving, shifting center and pointing in the direction you need to go and lifting the foot placing it back down. I've seen too many injuries resulting from torsional loads on knees from pivoting on heels or balls of feet. Primarily moving your hips and shifting body weight correctly in the direction you want to go and leading from that area, then moving the foot not under load makes for safe movement and a stable platform.
I keep telling people who train with me that the only place where they could glide their feet and perform big smooth taisabaki, moving and turning the way you see in aikido is, well, only while barefooted doing said aikido indoors in a nice smooth tatami. Outside, with shoes or in different terrain, it doesn't work as well. Certainly old battlefield-oriented kobudo, would have used more "stepping" and non-committed load while turning and moving. At least in the koryu I know of I have not seen mentioned turning from the balls of the feet or from the heel.
When I turn, say to deal with things happening at 90 or 180 degrees, I'm currently training to move from the center and move everything together while lifting
the legs to place them where they should be to deal with incoming/outgoing force. I don't really think about turning on balls of feet or heel anymore, but if I were to guess I'd say the turning is happening more at the center of the foot as a natural extension of the whole leg, or, more likely the whole foot turns (the load is spread on the whole foot). It's less "elegant" when I do aikido as I don't slide my feet that much anymore (there's more lifting or "stepping"), but I also train a lot on wooden floors, concrete floors, smooth surfaces, sticky surfaces, outside on lawn and dirt, and with shoes, so I had to find a way to move that would work in all scenarios.