Photographing their art is a great idea – I've seen some parents put all those photos together in a photo book at the end of the year. For the art they've put less effort into, I save them in a box and use them for scrapbooking and collage projects. (My nieces and nephews are young though, and don't care that I tear up their work – that may become an issue later!) For the scuptural projects, I use the most complete ones as decorations, either year-round or as Christmas ornaments. I also set aside one spot in my house where their art projects can go on display for a month or so, then I either save, reuse, or recycle them after that. I also got a portfolio book to put their paper art in, and kept it in my living room; they were tickled pink to see their art on display, and loved to go through that book. Maybe each child can have their own portfolio in their room!
Why not make a collage of your kids art to showcase their abilities and then dispose of the leftovers. So your kids feel like you appreciate their work and yet you’re not drowning In drawings
There's an app called Artkive that helps you photograph/document your kids' artwork. I've used it in the past and it's a great way to alleviate the guilt that comes with tossing out art projects.