The Z80 had two hardware features that made it possible, and that nobody here has mentioned yet:
1: two sets of working registers, with a one byte instruction to toggle between them. I instruction cyclke to context switch between application and interrupt handlers. Only the TI 9900 came close with its in-RAM working register sets.
2: hardware vectored interrupt dispatch, fully suppported by theor accompanying peripheral line. Just a few clocks from raising an interrupt to executing the first line of code (typically switch context then ...) of not only the device but it's reason for interrupt code. No code wasted interrogating bitfields and scanning registers. 2 usecs interrupt response time. Faster than an Intel i960 with its 50MHz clock, that came along later.