Imagine when 2,000 years from now, some alien civilization uses its advanced technology to reverse engineer all the private keys and take the BTC. 
2000 years! Quantum computers will probably exist before then, and this is the sort of problem they eat up. Then again, they've been fifty years away for the last fifty years...but we're really close I promise!
Come to think of it, the fear that quantum computers can find private keys ought to harm confidence in cryptocurrency once it becomes feasible that the government might be there already. It's totally going to happen, it's just a matter of time. I know cryptography for the purposes of secure communication will simply move to symmetric algorithms with quantum key distribution to preshare the key, but I wonder how cryptocurrency will adapt. RSA being broken sorta breaks their entire model.