It's not so much the emulators that have latency, it's the platforms they run on that have mostly been optimized for throughput and battery life for the past ~20 years. It's possible to get low latency on modern systems, but it requires relatively advanced and often non-portable techniques to fight the system's attempts at "efficiency".

Where FPGA really shines is in producing a consistent timing model and the associated performance quirks (such as slowdown in video games).

This is true but depending on personal preference/perception and usecase it might not matter. If you really care about latency for twitchy old-school games, a MiSTer (or a real Amiga!) and CRT monitor would be ideal.