I agree that wire (like rigid circuit boards) is almost always the right answer. But, for example, I think flex-circuit interconnects would have worked with a custom LED strip I was working on with someone else. The idea was a set of 3 boards that would let me drive RGB LED’s using a couple PCA9922 shift registers, but the number of wires we’d need between boards (8 I think) made it too big. (You could nearly indefinitely chain sets of 3 boards together and use it as a big shift register.) Thin wire was fragile and labor-intensive; multi-conductor wire was too big. The goal was to make something wearable without having to worry about failing electrical connections, or without having to hand-wire 8 threads between each board.
I guess I find that 8-10 conductors would cover 95% of my needs for low-current, flexible connections. When wire isn’t the answer, I don’t have an alternative.