or else you run into the problem that over a distance of hundreds of miles, a human will actually be faster than a horse.
Stuff, nonsense, stuff and nonsense, and did I mention nonsense?
It's all very well to compare horses vs. humans on tracks designed to make humans wearing nothing beyond running shorts even be competitive with a horse in a straight up race (and even then, horses mostly win anyway) - but please, I beg you, name me an infantry force that actually carries its own supplies, with a mobility range of hundreds of kms that horse archer armies could cover routinely? You don't have to be faster than the horsemen, even, just actually
able to cover the distance.
Or, you know, don't bother, because there are
none. The things that come closest are armies that marched from well-supplied fort to well-supplied fort along paved roads and even so it took them weeks to do it.
Russia's a great example by the way of a place that always had both cavalry in the eastern style as well as a sizable infantry component. Well, the infantry used boats to get around on the major rivers. They had do, otherwise they'd be strategically useless. The cavalry? The cavalry walked.
And kept pace.
First, of course, they are terrible at taking fortifications (they tend to lack range compared to foot archers, and forts make it MUCH worse because they're also large targets). Second, they are terrible at holding ground. Third, they have issues using their mobility in broken terrains (i.e. most of Germany, at least).
Of course, we have plenty of information that suggests that when confronted with archers in defensive positions, horse archers simply use their common sense, dismount and use heavier bows (horse bows also come in different draw weights, the heaviest ones are only slightly lighter than the heaviest infantry bows). The Ilkhanids did that, the Seljuks did that, the Crimeans did that, the Russians did that, the Qing did that. It's very well recorded.
It didn't always work against a determined defender but it wasn't a turkey shoot for the infantry force.
Naturally, Silesia and the Yangtzi Valley and Zalesye are presumably all open flat steppes oh wait no.
So on come your horse archers, against an equal number of archers backed by an equal number of spearmen with shields (because archers and spearmen are far cheaper to maintain). Good luck to the horsemen.
So basically exactly the setup at Mohi, right? We actually do know how that one ended. Not the way you suggest.