Thought experiment: how many arcane spellcasters in a fantasy combined arms army

[Eldan]

No, I don't think that makes any sense. Planes are expensive compared to individual humans. Wizards are not inherently so expensive compared to humans. A low level wizards, especially level 1, isn't that expensive at all really. Also note that modern planes have tended toward higher tech and greater cost; the plane to serviceman ratio may have been different in earlier eras.

A better point of comparison for arcane casters would be the heavier equipped modern infantry; ie the ones that have mortars, bazookas, anti-X missiles. Also the field artillery.

They are quite expensive to train.
Consider: a first level fighter is expected as their starting equipment to have scale mail (50 GP), a longbow (75 GP) and a greatsword (50 GP), plus assorted small stuff. Let's call it 200 GP.

A wizard? A blank spellbook is 15 GP and a component pouch 5, but they also scribe every spell in there. But they also have to scribe all their spells. That's thousands of GP.

I think that's a reasonable approximation for training costs. You can get 5-10 fighters for the cost of one wizard. Now sorcerers and clerics, those are cheap for the power output. You want magical bloodline breeding programs and free religious education.