It's definitely possible to write an emulator without unsafe code. Here's a toy gameboy emulator I wrote a while ago in Rust without any unsafe code: https://github.com/simias/gb-rs
Here's a very incomplete PSX emulator with only a single unsafe (which might not even be necessary anymore, I haven't updated the code in a while): https://github.com/simias/rustation
Or are you saying that a dependency that I use happens to use unsafe code? In which case it's true but then by that definition it's effectively almost impossible to write 100% safe rust since the stdlib itself contains a non-negligible amount of unsafe code.
In those old 8- and 16-bit machines all components usually ran completely synchronous for each clock tick, for instance if the video emulation runs out of sync with the CPU emulation for a tick or two, a write from the CPU to a video hardware register might not make it in time and you get garbage video output.
Modern asynchronous systems may need less (relative) host system performance for emulation, because the timing requirements between the different hardware components are much more relaxed.
I haven't written an emulator for the NES yet, but on machines like the Amstrad CPC or C64, the CPU can reprogram video hardware registers (like color palette entries) at any time, for instance in the middle of a scanline. When this is off by a tick, you get the color palette change a couple of pixels late or early.
If CPU and video chip emulation would run on different threads, they would need to sync with each other a few million times per second, that doesn't sound like a good idea. If synchronization is only needed once per scanline, or even per frame that's an option of course. Often this is good enough to run some games which didn't go too close to the metal (again this is only from my experience with home computer emulators, haven't done NES stuff yet).
Parallelizing through SIMD might be an option though (one can pack a lot of 4- or 8-bit counters into a 512-bit register).
Threading in that case would likely mean several orders of magnitude of performance degradation.