Thats really ghe best option IMHO. I have the NI S6 synthweighted controller and a Kurz pc3x 88 weighted key synth, which has great on board sounds in its own right and I can jus turn it on to play thru amp or interface and monitors withoug dealing w computer if I just want to bang out an idea.
Hadn't thought of it before (and I do think the Privias offer a lot for the money), but if you are willing to go used you could prob pick up a weighted synth from Kurzweil, Roland, Yamaha or Korg that will frankly blow the Privia out of the water in terms of all around capabilities AND will be at least equal, probably better, for piano. Downside being a steeper learning curve and, of course, no built in speakers but although the speakers sound pretty good, you probably woundn't use them in a studio setting or live setting.