I don't know about physics, but it's definitely not true about electrical engineering. The Fourier transform is one of those things that is absolutely fundamental to any branch of electrical engineering, you run into it when doing anything, from microelectronics to power distribution. And there's typically no way you get an EE diploma without a soul-wrenching course on signals & systems.
As a personal anecdote: I ended up taking three courses: one on signals, one on systems, one on circuits (...and systems!). During those troubled uni years, trying to see if I can still remember the Fourier transform was my "am I too drunk?" benchmark. When I could no longer do it, I went home.
And there's typically no way you get an EE diploma without a soul-wrenching course on signals & systems.
Similar to the person you're replying to, my education is in computer engineering rather than electrical engineering. I took the "signals and systems" course which was a treatment of Fourier series, Fourier transforms and convolutions. Since the final exam was open book, I did well by primarily being able to quickly look up the information relevant to each question on the exam. Convolutions did seem a little bit convoluted but the course didn't seem particularly soul-wrenching (compared to, say, the intro circuits course or the intro electronics course). Perhaps I was spared the soul-wrenching bits (e.g. I took a stats course instead of the course on random signals) or perhaps my university's electrical engineering department is subpar.
The soul-wrenching part depends a lot on the professor, I suppose. My Signals teacher was absolutely stellar and put a lot of effort into giving us a solid understanding of the theoretical underpinnings of her course, so it was pretty math-intensive. The exam, as I remember it, was pretty modest in terms of difficulty, but the course was pretty hard. I aced every homework, lab and exam, but that's largely because I loved that course. Everyone I knew struggled with it. It ate a good 4-6 hours off every week, in addition to the time spent on assignments & co. (sometimes more, but by my own making, i.e. because I'd hack on something alluded to, but not taught in that course. Like I said, I really liked that class).
My Circuits and Systems professor, on the other hand, wasn't too interested in this. He obviously cared about us knowing the math, but insisted that he was teaching a Circuits class, not a Mathematics course. His course seemed a lot easier as a consequence. I was never that good at math. I learned it because you can't do engineering without it, but it has always been my weak spot.
(Edit: I don't mean it in the "how much is 12% out of 45 USD? zomg I suck at math" way, that's 5.4 USD, I'm not an idiot. I mean it in the "vector calculus made sense, I think, but I could never have made a career out of it as I did with writing software and designing electronic devices" kind of way.)
My Systems professor was smart but had long stopped caring about that course and his students, so I learned most of the material by myself. At the time, I thought he was an idiot, but I've come to understand him in time. His course wasn't too torturous, largely because I skipped most of the classes.
Most of my colleagues (particularly those in CompEng) didn't take separate courses on Signals and Systems though. They had a single, bigger Signals & Systems course, that was taught by a couple of hardcore professors, both well into their sixties and both of them very draconian. One of them also taught an introductory Electronic Devices and Circuits course that I took, so I knew him firsthand: he was a very good professor, but he was about as flexible as a chopstick. An year when less than 1/3rd of his students failed the final exam was a really good year.
Or, and just guessing by the open-book part, that program didn't have you derive convolutions from scratch, but just use formulaic derivations for common cases. Which is useful and all, but not the same level of soul torture.
As a personal anecdote: I ended up taking three courses: one on signals, one on systems, one on circuits (...and systems!). During those troubled uni years, trying to see if I can still remember the Fourier transform was my "am I too drunk?" benchmark. When I could no longer do it, I went home.