On the contrary, there is:<snip> I would just like that there also exists this kind of alternative approach for many subfields of physics. And often it doesn't.
General introduction- https://www.amazon.com/dp/1107602602/?tag=pfamazon01-20
Fluid Mechanics- https://www.amazon.com/dp/0199679215/?tag=pfamazon01-20 (2 volumes)
Electromagnetism and optics- http://www.worldscientific.com/worldscibooks/10.1142/9251
These are just the few I have within reach. I'm sure if you search arXiv you can find monographs as well.
As to your question, why is Physics not generally taught that way, my unsatisfactory answer is that I'm not familiar enough with the math to plausibly teach the material. I can learn it (and I have been learning the material, after a fashion), but I'm not currently prepared to teach that way.
You would (or at least should) definitely appreciate this one: http://www.springer.com/us/book/9780387989921
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