Why would they have them? Firstly, skyrim's legion recruits from Skyrim. Secondly, the Empire's Synod is about politics. They don't teach. You learn that from J'zargo and that chick who is second in command of the college.

Because they show some of them in the beginning of the game? Jezz

So they might have been some of the dudes who accompanied Tulius north. They also probably died.

But they aren't. If anything, they are a poor representation of them and how they would act in combat scenarios

Yes they died in the attack at helgen I think. Well almost nobody survived that.
But it is known that the legion always use mages or battlemages or that sort of crap.
And they may recruit some from Skyrim but most of them come from Cyrodiil.
So it is just a missing from them, I think.

Based on what?

Not all of their forces are from Skyrim, and even if they were, there are people in the province that practice the art, Nord and otherwise.

Also, if establishments in the Empire (either the Legion or otherwise) don't teach combat magic, how do you explain the fact that we clearly see mages fighting for the Imperial Legion? It's not a question of "Why would they have them?" They do have them! We saw them!

Skyrim's legion can't draw from Cyrodiil's pot. The empire is refusing to reinforce them, telling them to recruit locally.

And while the Empire was once well known for battle-mages, the game tells us this isn't the case anymore.

Maybe they learned from somewhere else? Could be that they were actual members of the Synod, ordered to travel with Tullius. We don't have enough information to guess why they're there, but the information we are provided with suggests mages aren't common place in Cyrodiil anymore.

Based on the siege of Whiterun.

The legion organization worked better in field battles and that's what the army of the time mostly stick to.
When then the Roman republic invaded the northern parts of Europe, which, at the time, was covered by dense forests, its legions were sometimes humiliated by the attacking 'barbarian' tribes who used the ground to their advantage.

That's how the legendary figure of Julius Cesar came into play. Like Napoleon several centuries after, he was the kind of man who could lead an army, no matter against what odds or outnumbered, to victory by improvisation of novel tactics and by understanding the weakness of an enemy strategy the moment he saw it at works.

Where?