It solves the problem of not having to rely on a central bank to maintain the value of currency. It may seem unnecessary in the US, but pretty damn useful in countries like Zimbabwe where the privilege to print money has been abused. The opposite problem of deflation (a la Japan) seems more likely to hit the US. As population declines (and with it the demand for housing), it'll become necessary to destroy money with negative interest rates to reach the target inflation, boost investment, and check unemployment. But that's damn difficult with currency notes. And there'll be political opposition to any effort to target higher inflation or fiscal policy that has the government borrowing and spending more. The behaviour of UK and EZ governments and their austerity policies (especially towards Greece) do not inspire much confidence. An alternative currency might start looking attractive when that happens. Bitcoin is even more deflationary and won't help. But some other cryptocurrency could.

It's also a matter of principle. There are some who don't like the idea of central bank monopoly. A competing currency could be beneficial even if the only thing it accomplishes is keeping central bankers more vigilant and honest.