Basically these boxes weren't made to last which means if you find one in very good or excellent condition it has some extra value.
If you don't use the box, just put it up in a friendly environment to preserve it, maybe decades later you'd have something to show off and brag about.
PS
The box my Dad's Deville came in still looks pretty good for a fifty year old plastic box more suited to a watch of one tenth the value when new. Its been kept out of sight in a drawer still in its outer card board box which has also held up very well. Had it seen daily use it would have ended up in the trash bin thirty years ago.
Mom's old Bulova came in a stylishly Art Deco, possibly bakelite, box that still looks very nice after seventy years or so, though it saw much use with no attempt to preserve it.
Some boxes from that era are true works of art.