Well... you are wrong. Both software emulation and FPGAs depend on the knowledge and skills of the developet making them. They can be as good and as bad as they can make them. There is nothing inherently better for either, especially when it comes to accuracy and compatibility.
Yes and no. In emulation, a lot of problems come not from incorrectly emulating behaviors and functions, but difficulties with the timings and making it all work together. This is especially true for the Saturn, which uses dual CPUs and dual graphics chips that overlay on each other. FPGA has some big advantages in this regard.
Cycle-accurate emulators with 100% compatibility do exist for many systems, like SNES, GBA, NES, and Genesis. But most emulators don't work this way because it's simply too demanding to do with more complicated systems. It doesn't really exist past the 16-bit gen. Duckstation is pretty close, like 90% there. Definitely "good enough" that most would never spot a difference.
Now, that said, there are limits to what MiSTer can handle as well and PSX and Saturn are scraping the upper boundary of those limits. So Saturn is a real battleground where MisTer could prove itself superior in a concrete way.
FPGA isn't necessarily 100% accurate in the absolute sense either, like you pointed out. But certain things are a lot easier with FPGA.
Personally I do like the ease of use of emulation, and the broader system support. I have a handheld/console set up with a Pi and then dedicated emulation drive in my PC focused on accuracy and including newer systems. But MiSTer is closer to real hardware in some ways and I get the appeal, it just needs to mature a bit and get a better front end.
