Oh dear! Is this really an issue?? I have the exact opposite problem! I can't throw even the smallest piece of fabric away and I have tons of scraps and strings and crumbs! I keep making quilts for shelters - human and pet - and I never get to making quilts from my new fabric!!
It is as though with each new scrappy quilt I make, I end up with even more scraps!! I just vowed to make my next quilt out of some of my new, untouched fabric because I am always buying new fabric and not using it! I just can't resist buying it but my scraps have a hold on me!! I love doing QAYG (quilt as you go) quilts with my scraps and string quilts too and patchwork quilts are great for using up your one and two inchers!
Yes, I am a fabric-holic I confess...
Done rambling for now! Sorry, your post just got me going!