Why does the home button in the iPhones have dedicated terminals?
Speculation as none of us are Apple engineers and if we were, I doubt they could freely talk about it.

But the most likely reason is that allows for separation of parts, easier assembly and a lower replacement cost. Had the home button, which in the pictured 4G iPhone is a simple button and not the newer fingerprint camera, been using a fpc, it would require a connector at the top like the others. The top of the iPhone is pretty full as is. It would also add another failure point in assembly as the flex cable at the top is likely to get pinched. And it would have likely been made part of the display assembly meaning a broken button would mean replacing a 100 + display.