I think this is a pretty dishonest way of framing it. It's not just bitcoin, our entire system for secure communications across the internet (SSL/TLS etc.) is built on the assumption that P≠NP.

If someone were able to prove P=NP and come up with a practical exploit that made bitcoin valueless, it would also spell instant death for Ebay, Paypal, Amazon and a few hundred other small companies. Not to mention that all internet banking would have to be taken down very quickly.

In summary, it would be such a huge shock to the economies in all industrialised countries that it would make the 2012 financial crisis look like a minor inconvenience. Nobody would be concerned with "ah shit, my BTC is valueless", they'd be concerned with "ah shit, there's a run on the banks to get physical money and I will probably starve."

It's pretty much the same story for anything that depends on cryptography, including virtually all transactions involving normal currencies.