My take on it would be that there are different effects, mechanics, engines, encryptions, and styles as to how a game is created. The way I see it the PC games Half-Life 2, Gears of War, and Elder Scrolls 4 Oblivion all have different engines in order to be created. These engines have coding styles and carry out instructions differently than each one; i.e half life 2's engine tends to be very streamlined, compatible, and easy to mod but tends to lack in the GFX department when it comes to special effects, detail etc. GoW is built off the Unreal engine which, imo, provides very grainy graphics, great effects, and its a different style altogether sacrificing compatibility and performance for these things. Many games are based off of this but not all. In my eyes the creators of the ps2 games do the exact same thing and some implement creative new flashy effects or a new type of encryption (Tri-Ace) or a new type of physics a new type of way to render an FMV that type of thing. Seeing as how the creators don't have documentation as to styles of coding Sony allows to be used on their machines they have to guess and do their best to backwards engineer things in order to play a game.
Idealy, PCSX2 will have a database large enough to be able to play whatever game is thrown at it because it knows how to interpret all kinds of code and it knows what to expect. Right now, if a game throws a curve ball at it, it has no idea how to handle it and it crashes, doesn't run, gives an error etc. Relatively speaking, FFX and the other examples you gave aren't complicated games from a coders stand point; they don't have major transperency, shadow, collision, physics, shader coding that needs to be emulated. To be honest, the graphics in those games are just high resolution versions of the PS1's with some added fluff.
In short, each game is different and the emu does what it knows and right now it doesn't know a couple different things here and there.
Thats how I view it anywho, I very well could be wrong and I apologize for any missinformation no I don't have any method of backing this up ATM, but feel free to correct me
. Just my two cents.
@foulusama. You beat me to it as I was typing my story