I think it is good idea to keep it around. You never know when it might be useful. If you don't want to keep most of the physical paperwork you might consider scanning it, encrypt it and then keep a few encrypted digital copies around. Anyway, keeping the documents might be better.
As an example of usefulness I applied for a copy of my A file through a FOIA request and they sent me a letter asking me for copies of document or documents I received from USCIS in the past, so they would be sure I was the right person. They also asked me for my parents names and birthdates. Of course I know their names and birthdates, but I wasn't sure if the GC paperwork had full names, or initials. It is good I had the right documents to refer back. Could I have solved this in other manner if I didn't have the paperwork? Sure. Would have meant more work to solve it in another way? Probably.
My 2 cents.