I wonder if it's because the PS3 loading times are never long enough to have those loading screens. Judging on videos of the Ami version, no PS3 loading sequence ever lasts long enough for her to start singing (I think). But it doesn't change the fact that I saw Azusa for while before she simply disappeared. Maybe I should try playing through the extra episodes again, though I'm sure others would have done the same thing before.
Actually, on benching, the PS3's actually slower than the X360 for loading. Yep, I recorded it at one point cause I wasn't sure myself. Granted, this is against a X360 installed version, and have no idea what it'd do against a disc only.
Azusa only shows up at the end of a story run, and only when you gain trophies. Depending how many you get that run, she'll do a series of expressions. In short, if you get a lot of trophies in one go, you'll even see it completely loop.
I suspect the main reason they took her out is simply the fact even on a straight run (no installation) on a X360, you normaly do not hear more than 1/3 of the song. You LITERALLY have to damage the disc to get it to loop.