"You cannot ship insured without the original boxes. I’ve seen manufacturers charge $400 for a replacement box."

Say what? Where did you get that information from? I've bought and sold gear many times without original boxes and always insured!

I have struggled with this question for the last fifty years. My observation has been that space available increases over time as one becomes more wealthy. My conclusion has been that keeping high end audiophile component boxes is appropriate. 
 

You can toss the microwave box, the LCD TV box but audiophile gear lasts a very long time and should be kept. I would not rent a space for them, but I would carefully stack them out of the way. If you have chosen high end audio, I am guessing you have not chosen a dead end career… so over time you will be rewarded and space will become available in your life. 
 

I now have a huge storage area where I keep all my audiophile boxes. When I need them they are there. Every 7 - 10 years I trade up and the components are boxed in their original containers and traded in. 

Can I discard high end shipping boxes, and still sell in the future?

Yes, but you will get 10 cents on the dollar instead of 15 cents on the dollar.

I learned the hard way to keep the original boxes wherever possible.  Not only do the original boxes perfectly protect the equipment and have styrofoam inserts that perfectly fit and therefore protect the equipment, but to have expensive gear, especially speakers, packed in new boxes and bubble wrap is pretty pricey itself.  And if it isn't done right, you get a mess when delivered. That has happened to me twice, (receiving and selling) when I lived in a condo with minimal storage space.  Now that I am in a house, every box has a nice storage spot on shelves that I built along the ceiling of the garage.  I'm not sure that I would pay less without the original packing, but it is definitely a selling point.