The real question is, "Do you have the room to display all of your collection at once?" If not, then ask yourself, "Where will the toy go when not on display?" If the answer is, uhh sh!t, what now, then you will need to keep the boxes. If you have unlimited shelving, then it doesn't really matter.
As for flattening them, I don't see why not, if you don't plan on selling them, then do whatever you want. However, if it comes down to throwing away a vintage G box and insert, you may want to try selling it on eBay first. Sustain you buying collection by selling the stuff you don't need.
Oh, to Goribus, nice quote under your sig. I saw Lamb of God, Trivium, Machine Head, and Gojira this past weekend. Firggin' killer show!