High end transformers and circuits are built for isolation, high bandwidth, and low distortion, they are not designed to go into saturation. To keep a transformer just under saturation requires compression. IMHO I think what most people associate with transformers is the compression used by the circuitry around them.
Thought experiment:
Every dynamic mic, like a Shure SM7 has a High Imp / Low Imp transformer in the mic. These are actually pretty high quality transformers.
The Shure transformers which can be had for $20.
For a guitar cable take two transformers wired as:
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And one of these:
https://smile.amazon.com/Hosa-GXX-144-XLR3M-Gender-Changer/dp/B000068O4J
Shure A85F <==== cable ===M to M adapter => Sure A85F
This provides Isolation, Passive loss, Bandwidth limitation, And if driven high on input core saturation, and "Two" transformers. If this sounded so great, you'd be seeing guitar/bass cables made like like this. And they probably would sound great with some compression to keep them just below saturation.