Since you mentioned z80, I happen to know just the perfect example of the platform where this kind of precise emulation is sometimes necessary: ZX Spectrum. The standard graphics output area on ZX Spectrum was a box of 256 x 192 pixels situated in the centre of the screen, surrounded by a fairly wide "border" area filled by a solid color. The color of the border was controlled by outputing a value into a special output port. The computer designer's idea was that one would simply choose the border color that is the most appropriate to what is happening on the main screen.
ZX Spectrum did not have a precision timer. But programmers quickly realised that the "rigid" (by modern standards) timings of z80 allowed one to do drawing that was synchronised with the movement of the monitor's beam. On ZX Spectrum one could wait for the interrupt produced at the beginning of each frame and then literally count the precise number of cycles necessary to achieve various effects. For example, a single full scanline on ZX Spectrum was scanned in 224 cycles. Thus, one could change the border color every 224 cycles and generate pixel-thick lines on the border.
Graphics capacity of the ZX Spectrum was limited in a sense that the screen was divided into 8x8 blocks of pixels, which could only use two colors at any given time. Programmers overcame this limitation by changing these two colors every 224 cycles, hence, effectively, increasing the color resolution 8-fold.
I can see that the discussion under another answer focuses on whether one scanline may be a sufficiently accurate resolution for an emulator. Well, some of the border scroller effects I've seen on ZX Spectrum are, basically, timed to a single z80-cycle. Emulator that wants to reproduce the correct output of such codes would also have to be precise to a single machine cycle.