Disciplined English (and Welsh) archers properly used would chew up a steppe horde formation as long as the numbers were not to heavily against them.
Based on what data?
They accurately outranged the recurved bows
Based on what data?
Even something as simply as iron - you can make a lot of arrow heads with the same amount of iron you need to make a firearm
True. Self bows and their ammo even at their priciest are the cheapo option.
and of course perfectly effective arrow heads can be made of bronze, or even bone/stone.
If people aren't wearing any armour, maybe.
You can use firearms from horseback its just hardly effective. Horses never really take to the ding of firearms and it takes a lot of skill to keep the horse steady. The tactics you cite are part of a combined arms approach- cavalry supported by artillery and infantry. This is not possible for steppe nomads They are all cavalry units. Finally, with few exceptions, the use of wheellocks from horseback last briefly. The use of cold steel is pretty exclusive
The Muscovite gentry horsemen (a universal soldier if there was any for about 300 years) were basically mounted bowmen for most of their existence, but despite their conservatism and the cultural power of the bow, they ended up using pistols and short-barreled firearms same as the regular Muscovite dragoons and reitars by the late 17th c. It happened even earlier with the Ottoman cavalry.
It could well be argued that this had to do with change in tactics as a whole, of course, but we aren't exactly swimming in historical examples, so we have to account for the few that we do have.
As for the rest, it's basically what some people said: it's not the muskets, it's the artillery. A few pieces of field artillery and a cheapo earth-and-timber-walled fort is too much for even several hundred men without artillery. Better walls and better guns just multiply the advantage, and the sedentary state can start restricting the area where the nomads can live and dominate.
Mass encastellation was a valid strategy even before powder arms, but powder arms are more accurate, longer ranged, and vastly more lethal than anything else before them, and the rate of arrow shooting is offset by the costs of lugging arrows around.
As for why nomad armies can't afford cannons: same reasons why individual knights and lower nobility couldn't afford cannons during the early modern era in Europe: the cost of building and running one large gun was phenomenal relative to the cost of hiring regular fighting men. None of the nomadic states commanded that kind of resources.