I make all sorts of things that aren't meant to be handled or handled very much (think potholders, mug rugs, and wall hangings), as well as things like baby quilts that get more use. In every case, I PP onto the lightest non-woven stabilizer/interfacing I can find and then I just... leave it.
I like the stability (duh) that it gives the finished pieces and I especially like not having to deal with taking out the paper. I tried piecing onto paper and taking it out... and swore never to do so again.
If you use the super-thin interfacing/stabilizer, you can hardly tell it's there.
Works for me! :)