Eames 670 in box  

The reasons why it would be feasible couldn't possibly be as interesting as the reasons someone could give for why it would not be feasible.
The end of this video shows how Herman Miller originally shipped the chair and ottoman in two relatively small boxes.
https://www.youtube.com/watch?v=9SWL4gTQfTA
 

Very feasible and it makes sense to reduce shipping cost, except it is not practiced because of the stigma knock down furniture has and most people who paid thousand of dollars plus white glove delivery fees for something like the 670 chair and ottoman expects it be fully assembled when delivered to them.
I am not a purist when it comes to vintage stuff but I did get a lecture from someone at the Eames Office for removing the screws of 2 very rare and early yellow stain DCM (I own) which fit in box acceptable as checked-in baggage in a domestic flight.  (bases where stacked and all the wood parts were individually bubble wrapped)

I've had two LCW shipped disassembled. Oh the excitement at putting them back together!
On another note, is the Softpad Chaise a potential disassembly exercise?

It is very normal to ship a 670 disassembled. I received them like that many times and I shipped them like that many times. Where possible put screws back in screwholes after disassembling.
Make sure you use a screwdriver that fits well so you do not damage screwheads.