Tanya has to organize her own battalion of mages because the ones that exist do not suit her that is not a useful analogy.
The Germanian army certainly had its issues with prejudice against women when it first began recruiting mages. However, the brass would never tolerate a unit that refused to accept half the mages in the recruitment pool. Iomedae was operating in a less centralized world, where private military 'orders' were legal and could decide whether and on what conditions to fight in the war. Perhaps Taldor was incapable of conscripting its mages because of political dysfunction and infighting, or perhaps the central government simply could not enforce its power over the border provinces even in an emergency, Iomedae was from - somewhere Tanya can't place on a map but she doesn't want to bother the Nethysians for a political map seven centuries out of date.
Tanya is used to holding militaries to a high standard, but nations can behave idiotically no less than individuals. Just look at the Entente's internal politics which started this whole mess. (Tanya's mess, not Iomedae's.) A government that doesn't know or refuses to acknowledge that the war it is already fighting is an existential one that it is badly losing is - painful. Iomedae (more relevantly, her superior officer Arnisant, though he might not have been sufficiently high-ranked) did not resort to drastic measures and attempt to replace the incompetent government. But that is because she had a higher authority to call on; the god they all (nominally?) obeyed. Tanya... doesn't know how to apply that to her own situation. She could read it as an endorsement of them trying to do something anyway, but perhaps she shouldn't be reading the Acts as an endorsement of anything she ever did.
Intervention budget treaties constraining the gods are clearly a very important fact. It explains some things, and implies a lot of other things which Tanya hasn't thought through yet, and also raises a host of additional questions. To begin with, wouldn't the very first communication to your mortal followers explain divine budgets and how to use them efficiently? However much that communication costs, surely it will pay for itself by its very nature? And if you want to send a powerful agent to fight in a war - a big intervention! - surely communicating that you want to do that and that they should call her is a tiny one in comparison? How can you get anything done by relying on one of your mortal followers to happen to ask you whether you want to do the thing you were planning to do all along?
In fact, if she's such a powerful archmage, why can't she come over herself? If the mortals call her first, does that mean she can do anything she likes and it doesn't come out of her budget? But then, why didn't Taldor regularly call every Heavenly ally they have in case they wanted to come help until one of them accepted the call? Arazni was in a unique position as Aroden's herald, which made her an obvious target... maybe the calling spell is extremely expensive, and so is the Commune, but why can't you do a regular Sending to check if they want to be called? Tanya is lacking too many facts to make any sense of the story being told here. (Or perhaps divine budgets are extremely complicated, the book doesn't explain them well enough for Tanya to reason about them, and only a unique genius like Iomedae could have figured it out.)
She's not here to read a military history of the Shining Crusade, though, and the book clearly isn't one. What are the philosophical or moral points being made by the story?
Iomedae doesn't automatically trust her fellow mortals, any more than she does her god. She has exacting standards and she is unafraid to challenge existing institutions and if they don't suit her to found her own. When she (correctly) thinks the higher-ups are failing at their jobs, she bypasses half an army's worth of a chain of command to appeal directly to the supreme commander (and is proven right, otherwise you wouldn't be reading her story).
Not only is she almost always right, she is always - taking initiative. Her accomplishments so far aren't as a great soldier or mage or tactician, someone who achieves unprecedented success in carrying out the plans of others in a machine that relies on everyone doing their job. Not even as a great reformer; maybe that will come later once she commands the entire Shining Crusade, but she ended up with her own country instead of taking over Taldor and Tanya can begin to see why. She comes across as - an outsider. Sharing the organization's ultimate goal (victory over Tar-Baphon) as a personal one, joining the army only inasfar it serves that goal, and being unafraid to criticise it both implicitly and explicitly.
If that's the model the Iomedaeans strive to emulate, it's no wonder they wouldn't appreciate Tanya. And if that's what's needed to be Good...