Man, us QA people sure are good at poking holes in the methods or practices we don't like...
Not intended as an insult to any of us, we're all just set in our ways and worried about the potential gaps we see in other practices.
Personally, I like the binders. It provides immediate access in an emergency, lets you quickly initial and date to indicate you have reviewed the documents right on the document, and keeps everything in a designated spot.
My main concern with storing electronically and printing as needed was access, which is because easily 90% of the people in any of my plants don't have a login to access a computer. If people can overcome the access issue, great. Then you deal with how to document that you've verified every SDS electronically each year (or whatever frequency you set via SOP). Uncontrolled copies floating around randomly become an issue, so then you set the policy that every time you need to reference the SOP you must do it via a computer, and then people argue that becomes an unnecessary delay if there is an emergency. But then, binders create a delay as well as you have to send someone to run to the one or two spots you normally keep them.