As for why Photoshop does it differently, its implementation is more general purpose as it should look good both on electronic and physical media. Windows can get away with RGB anti aliasing because it only has (had?) to display on screens.
Yes, and since it requires an Operating System's support, there is little benefit for Photoshop to change the Font rendering mechanism, and it wouldn't know the order of the RGB lines, or other arrangement pattern (that's why it needs to be calibrated on the display one uses). Traditionally, Photoshop was used more for Pre-Press activities, and that would mean that Type is set at very high resolutions, where traditional anti-aliasing is enough if not already overkill.
Display resolutions were traditionally very low (1/4th or 1/3rd of visual acuity at reading distance), so they can/could use all the help they can/could get. But even with high resolution displays, there may be some benefit (still sharper and less stressful to read) for rendering very small fonts.
Cheers,
Bart