Just about every single situation where you'd ask "Why is this newer system emulated well while this older one isn't?" can be answered broadly with "Because some vital piece of hardware isn't well documented". The easiest-to-emulate consoles tend to have very common hardware, often full of off-the-shelf components. The Sega Genesis/Mega Drive runs an unaltered Motorola 68k, a CPU that's in
a fuckin' thousand things from the 80s and 90s. Is it well documented? Hellllll yeah mothafucka, here's a
PDF going over its instruction set, and a video tutorial on how to code some very simple Genesis software:
In fact (and this is from my distant memory, so take this with a grain of salt), there was a time when Genesis emulation was further along than NES, because the NES used a video card (PPU) that was designed in-house at Nintendo, so it had no external documentation. It was a black box. Of course, we're talking 1983 hardware designed by a then-toy & arcade company, so hobbyists managed to get it working in a good enough state for kids of the 2000s to enjoy their games in Nesticle. Meanwhile, the Sega Genesis' Video Display Processor is built on top of the
Texas Instruments TMS9918a, a video display controller used in a number of different 1980s computers. Here is its
patent, with full schematics. Of course, it's not literally an off-the-shelf TMS9918a, but an enhancement, though I couldn't find exactly how it was enhanced, or who enhanced it. Point is, plenty of documentation was freely available on what exactly made Sega's early consoles, which wasn't the case for Nintendo.
I don't know a whole lot about the PSP's hardware, though Modern Vintage Gamer mentioned in a video that its CPU is from the same family as the PS1, which explains both why PS1 games work so well on it, and partially why it's well emulated via PPSSPP. I'm sure it can't be that simple, though, or else PS1 emulation would be something just built right into PPSSPP.
So that's more or less why so many random old systems don't work as well as they should. N64 and Sega Saturn both have notoriously complicated architectures, though I think N64 is pretty well fully playable. Xbox was stymied for decades due to its GPU being some proprietary witch's brew, though there wasn't much of a push for it due to it having a tiny library of perpetual exclusives.