A thought that occurred to me a couple of weeks ago, but I was too disorganised to post at the time, is that I think the factors that modulate movement rates are different before and after the advent of mechanical transport. When an army has to walk, the likely pace of movement is sufficiently low that the ability of a commander and staff to make a plan and dish out movement orders is probably not a major constraint on the time it takes a unit to move from a to b. Once the internal combustion engine lets people zoom around at giddy speeds like 15, maybe 20 miles an hour, this is not longer true; and I suspect that the added complication of headquarters organisation and signals sections mean that very little time is saved in the distribution of orders, so the main limit on unopposed movement becomes the speed of tactical decision-making. As a pal of mine put it, “an army advances as fast as it thinks”. I have said “unopposed movement”, but there is also the point that for the last hundred years air and indirect fire have meant that moving elements can encounter opposition, and have their movement rates slowed miles behind the forward line of own troops.
All the best,