I have always been curious about FPGAs and I think I understand the concept, but what could someone provide some use cases for why you might want one (that aren’t calculating SHA-1 hashes)? As someone who understands microcontroller programming and wiring, what cool things could I do with an FPGA that I would have a hard time doing with other hardware?
It's kind of a stretch, but take a wall of addressable LED strips like WS2812s as an example. Color data is sent along one wire as precisely-timed pulses, 1.25us per bit.
You can drive a few strips using critical sections written in assembly, or misusing SPI peripherals if your clock speed can easily divide into ~2.4MHz. But you'd be hard-pressed to run dozens of parallel LED strips with a good framerate.
On an FPGA, you can just write an "LED" module and add as many of those modules as you can fit into the chip. You can also decide whether to include a simple CPU in the design, or use another method of processing lighting patterns.
They're flexible, but they are also expensive enough that it's kinda hard to find somewhere that they make sense. A "cheap FPGA" price point of $50-150 is still an order of magnitude pricier than a cheap microcontroller board ($2-10).