"Zero cost"... Aside from the cost of nearly every major hodler of bitcoin dumping them instantaneously if the 21 mil cap is put in serious jeopardy.
That is not "cost". Even if bitcoins lose all their value, no resources or concrete assets will be destroyed. The world will not become any poorer. Only, a few hundred thousand people who expected to get hold one day of mansions and Lamborghinis will see those hopes vaporize, and those assets go to other people instead.
This would be utterly wrong. There actually IS an "internal" value inside every bitcoin and it's the amount of resources (computers/miners/electricity) to build its block. As time goes by, the aforementioned "value" will rise because the difficulty to build one will be greater and the block reward will be halved. YES, there's a chance this "value" will be destroyed but not because of what you're claiming, but because you lost your wallet's password - or your computer got on fire; but your loss will add more value to the rest of bitcoins spread around the world.
You see, what you fail to understand (which is common sense to my way of thinking) is what would it take for somebody to use something as a currency. The keyword is "trust".