I didn't read all answers, so sorry if I'm being repetitive, but...
So the question is this: if BitBox existed, would the market value of BitCoins literally drop to zero? I tend to argue yes.
I tend to argue no. I find bitcoins better than gold, even if gold could be made "digital". That's because one day bitcoin inflation rate will be lower than gold.
I read somewhere that gold inflation rate is around 2% a year. I don't know when bitcoin inflation will decrease to such rate, but one day it will.
Something better than bitcoins, however, could come out, yes. Then people would slowly migrate, I suppose.