Crossbows are "upgraded", easier-to-use bows, not much more. While the first record of crossbows, if I remember correctly, depicts a stationary one, it was by no means a siege weapon. Unless by "siege weapon" you refer to a defensive weapon used during sieges (semantics, I know), but from the context that doesn't seem to be what you're saying.
I suppose I lumped all particularly heavy weapons into the category of "siege weapons" there. It doesn't help that I recall bringing down gates and walls in Total War games with ballistae... My point was that in both cases even the primitive precursors of the device were upgrades in their respective field. In the case of applied gunpowder vs magic, it's a distinct downgrade, as mages are the equivalent of early twentieth century artillery in a more controlled, man-portable form [...]
Except for being usable by expandable footsoldiers. Knowing how to fire a crossbow or a cannon takes a relatively short time to learn. Magic is a life-long commitment, and takes years of study to master.
The latter part of your statement also relies on magic being commonplace, which is obviously not the case. If it were so conventional, there would be no need to give soldiers weapons or armour in the first place. The reasons they're still supplied with arms, despite magic existing, is the same siege equipment would still be used and needed.
Magic does appear to be pretty common, and there's no indication that it's arbitrarily restricted to certain individuals who are just "born with the gift" or some other nonsensical idea. It would appear to require formal training or somesuch, meaning it ends up restricted to those who happen to buy such training or stumble into it, which would be much the same sort of circumstances that would restrict engineering and such.
It's pretty common, but limited to the with privileged? That's rather contradictory. Just that is does require training and studying means it's going to be restricted to those who can afford such luxuries, i. e. nobles, and the fact that there are so few magocracies (they do exist, yes, but not as many as ordinary-cracies) means that there isn't much of a culture of magic-using among them. Okey, so I realise I'm rambling a bit now, as well as jumping to conclusions, but yeah.
Furthermore, as I said before, I view the frequency of mages in the games to be a simple case of selective exposition. They're cooler, so there's more of them. And the reason the PC has it so easy when it comes to learning magic (buying spells, for example), is simply game mechanics. Actual studying is not fun gameplay, so it's handwaved away. The same reason you can become a master swordfighter in a few weeks, when in reality it would take years and years of training.
Considering that gunpowder was thought to have arisen from alchemical experiments by the Ancient Chinese searching for an elixir of immortality, I find it extremely dubious that the people of Tamriel wouldn't stumble upon it as well.
There's a good reason I said "proliferation," rather than invention. There's a whole lot more to a device being proliferated, studied, and improved than it coming about in some wizard's laboratory. If I recall correctly the Chinese only used the gunpowder for fireworks, rather than anything practical, so the use as a propellant in a firearm is not as obvious as it seems in retrospect (and even the obvious use of "oh look, pretty colors and explosions!" requires the same level of expertise and training that producing similar (or more likely far nicer) illusions would).
People are taking the view that these devices are obvious. When you have people who can fly and rain exploding balls of fire onto their enemies, and they constitute the educated class, why would one think "hey, let's put this fast burning powder in a tube, with a little metal ball in front of it, and then jam a burning piece of wood through a little hole to launch said little ball really fast, so that maybe it hurts someone!"?
If magic were so common and easy to use, why would weapons exist? Like cannons, halberds and swords wouldn't be needed. Armour wouldn't be needed either, when you have shielding spells to protect yourself. But magic isn't available to the vast majority of people, so such equipment is still valuable. It's the same for cannons, catapults, ships, pulleys, plows, or most other equipment.
They aren't going to bother trying to train commoners. Why would one teach them how to fight when one can summon an already trained and equipped army of demons out of thin air?
Even summoning scamps is dangerous. There's no guarantee they'll do your bidding at all.
Edit: fixed the formatting, I hope.