My solution for throwing away most Kid Art without the guilt...
tl;dr
2-3 times a year I take photos of almost all of the art with my iphone. I use the Project Life app (.99) to make a couple of collages. I print the collages for $1.99 on Pernickity Prints and stick them in a scrapbook. I throw everything out after photographing it, except for 2-3 pieces I really, really love or that demonstrate some big progress. At the end of a school year I have 5-8 pieces I really adore. Those I keep in a file box with a folder for each grade. We have a designated box set aside and DD knows to put her art in it when she empties her bag. It might take me 30 minutes outside on a sunny day to do all the photos - and I can make the collages while I'm in line at the grocery store, riding in the car or watching tv. It takes minutes to make a collage in that app. My daughter loooves looking at her work in the scrapbook.
More info..
I was inspired by this video by Becky Higgins (creator of project life) about sorting kids work.
https://www.youtube.com/watch?v=JvFjiDcbpXg
Now, I don't feel guilty about throwing all the art out. I used to do this all by hand - taking pictures with my digital camera or using the scanner. Putting them in photoshop and using the project life templates for the computer. Some people even print the pictures. It took me HOURS, it was great, but it took a lot of time and I used to dread it. The app has been life changing. I look forward to it, it's fast. Doing it 3 times a year really helps me to only keep 2-3 pieces each time.
FWIW, I scrapbook other things with the app and my iphone. A recent camping trip, vacations, etc. I finished all the pages from our Disney trip on the 2hour flight home. Seriously, so stinkin' easy.
Video on how to use the app:
https://www.youtube.com/watch?v=t1Wpmm-wUmQ