We did this at our office some time back. There's more to it than you might think, and I wish we'd done it sooner. First, the cost savings is pretty significant. You've no idea how much paper, files, file cabinets, and sheer storage space for all this paper that's involved until you don't have to use it anymore. Add to that the labor cost of constantly running somewhere to hunt down a paper file, or the labor cost of having someone file away a stack of papers into that paper file. It really is pretty significant if you're in an office type environment that creates paperwork.
The problem is going from a hard copy environment to a soft copy environment. What do you do with all your existing hard copies? What mechanisms or hardware do you use for going from hard copy to soft copy?
We opted to implement our change on a going-forward basis. Basically as of a certain date all future paperwork would be soft copy. The idea being that (at least in our case) eventually the hard copy files would age into being obsolete and destroyed.
There's other issues. What kind of a system do you use to store it? Do you run your own server solution? Do you farm it out to a cloud-type solution? In our case, there was excellent proprietary management software geared to our agency, but what happens if that company goes under, or is sold?
All in all, it's an excellent idea but the solution isn't as simple as one might expect.