The two are not competing goals. There are plenty of emulators that aim for speed, so it makes perfect sense for someone to want to focus on accuracy. And yes, it is that important if your goal is to actually preserve things properly.
I don't know about the NES as I never had one, but on the C64 for example, a single cycle deviation in the emulation of interaction between the CPU, graphics chip and memory bus would make some effects impossible to reproduce. And similarly on the C64, people are still struggling to make the SID (sound) chip emulation as accurate as possible, as it used a combination of analogue filters that have proven extremely hard to accurately reproduce in emulation.
People casually testing these games might not care, but many of those of us who used these systems notice these flaws and appreciate that not all of the emulation projects focus only on speed.
