No, I will not. I often resell my old devices when I get something new, and people
like to have the original retail packaging. For some buyers, it helps relay that you take good care of your items (which yes, I very much do.) Phone boxes take up hardly any space, I tossed my current one in my small box of assorted cables. It's out of the way, but I know right where it is.
I save the boxes until I know the thing works and isn't going to be a quick RMA. I saved the boxes for my stereo for years as repacking it was the safest way to move it back and forth between home and college and beyond.
I use to save EVERY box from PC build parts, stack em and pile them into the box for the case. I always had a basement or storage space to keep it in though. Where I live now is pretty limited on extra space, including storage. The box for my 32" LG monitor and my 55" Samsung TV are in a friend's basement because as you said...the original boxes are the easiest way to pack for a possible move.
These are the only larger boxes I've kept lately...
Kitty condo. I did this after I got rid of my couch, which she hid under often. She loves the replacement though. Honestly I've been tempted to get them out of here but she's in and on it all the time so I've been hesitant, lol.