Everyone dislikes PaRappa 2 because it didn't do anything new, but TBH I think it's the best one when looking at it from a musical perspective. PaRappa 1 has memorable lyrics but the melodies are pretty simplistic and repetitive, and Lammy's attempts at multiple genres were admirable but had varying quality. PaRappa 2 on the other hand has awesome raps throughout, with the only real misstep being Hair Scare (one "repeat the same words over and over" song per game is enough for me, thanks).
As for your other point... due to the amount of time that's passed since PaRappa 2 and now, I think that they'd probably stick with the main series rather than a spin-off, to get people re-acquainted with the franchise.
