I used to put my discs in binders but over time I found it to be annoying.
I'm actually currently in the process of undoing years of using binders and moving to shelves. Fortunately my collection isnt as big as some peoples yet.
Using binders, finding this discs you want is harder, the binders themselves are big and have to go somewhere (not to mention cost more than youd expect, if youve not done this before), you can't really store them on top of each other because of the weight, and the actual physical process of removing/replacing a disc from/into its sleeve is just plain slower.
If you have a disc out for a few days you'll probably need to put the binder back to get it out of the way, but then you'll have to pull it back out, open it, and find the discs spot again later when you want to put the disc back. The binders themselves are susceptible to torn pages/sleeves and broken zippers. And god help you if you buy binders that dont have removable/rearrangeable pages. Even if you do, youll still be pulling out discs and moving them around within the individual 8-discs-per-page sets when you add new ones. You do some rearranging over time with shelves, too, of course, but carefully inserting/removing bare discs and binder pages is a lot slower than just grabbing groups of DVD cases off shelves.
Unless you want to spend time scanning the covers + any booklets and such, then you lose convenient access to the information and photos and such contained in them if youre boxing up the cases somewhere. Box artwork, booklet artwork, production notes, postcards, whatever else is in the cases, you wind up sealing all that away never to be seen again.
You still have to figure out what to do with any additional trinkets that came with limited editions, which, depending on what kind of shelving you use, you could otherwise just stick on the shelf alongside/behind the disc cases.
Worst of all, you lose the ability to show off your mass of shelves on GAF.
You gonna pull out and open all the storage boxes/tubs + binders anytime you want to take a photo? Pffft.