OK, I have no qualms with disclosing that I don't know everything. Send that to the 5 o'clock news if you wish
However, I have worked plenty with transformers, especially baluns and other impedance matching transformers.
And they are, in fact, reactive elements in an AC circuit, and must be accounted for.
They, in fact, have impedance characteristics and thus have an ohmic value
And they are, in fact, transformers.
Having thought the matter through a bit, I think you are strictly thinking of power transformers, and to be honest I am not sure I've ever given them as much thought as matching transformers, being my pet interest has always been radio, antennas, and transmission lines.
Adding to that, in my 15 years of maintaining electronic equipment at various capacities, I'm quite certain I've never had a power trasformer fail on me, though it isn't unheard of to have shorted windings it is fairly rare. So yeah, in that regard I haven't given it much thought.
Perhaps, if you will, without math, with more of a mental model, you could describe why there is no reactance accounted for in a power transformer's performance.
I am here to share, but believe me when I say I'm even more eager to learn.