To play PS2 games on PS3s now, all those games would have to be recoded, since the required hardware to support the software has been removed, and likely the system doesn't have enough processing power to be able to do live software-only emulation of the PS2. SE has already stated they are not going to recode FFXI again to move it to another platform, or upgrade it to use a higher version of DirectX on Windows, since it would be similar to coding a new game, and so they'd rather put out a fresh new game. They've already announced yet another MMO on top of FFXIV, and FFXIV is still being ported to PS3. FFXI only has a small development team remaining, and it's not the people that originally coded it. They're not going to recode the game when they can't even fix some of the issues existing in the game at this time.
Although most people have moved on, here's one of the articles mentioning the cancellation of XI on the PS3:
Quoting from the article:
"Initially we were in talks with a representative from Sony [to achieve this], but it appears that that person quit," said FFXI producer Hiromichi Tanaka, inducing laughter from the rest of the team. Tanaka also explained why it's a little more complicated to make the PS2 version work than, say, simply releasing some sort of patch or update for the PS3. "[Current] PS3s don't have PS3-side PS2 emulation, and it doesn't look like Sony has any plans to address that issue. For that kind of thing to even be conceivable, it would have to be on a disc. Digital downloads wouldn't work for this. The disc has to be in the system for the emulator to work."
Interestingly enough, Square also mentioned a Vita port, but that too got cancelled: