Laws don't stop criminals.
Yeah, that is shinny talking point of the NRA against gun control, but reality is, as always, more complex. Laws are a guide and a deterent, because if you violate them you risk facing consequences.
In our fictitious example, if banks, registered and well known entities, could be seized if they did not adopt the program you say it is needed to keep them in check, they would be... seized. Not something they want to happen.
Admittedly, BitCoin is trying to solve the technical problem
Bitcoin is not trying to do that. It wants to substract money from guberment oversight and control. That is different boatload of issues that it creates more than solves. The mtgox debacle shows the consequences of not having oversight and a central agency to help people who lost money.
But the problem remains that there's a thin wall keeping your money at the number it is supposed to be at.
If each dollar you have carried the accounting validation inside of it, as its own atomic data element, then potentially they are self auditing. You have $1,000 because you have 1000 vDollar files, and each vDolllar file has its own history and validation of how it got into your account. So if somebody steals it or copies it, it won't work for them because it won't contain the transfer record entry to their account.
Do you have examples of banks doing this?
It is possible that the product called BitCoin will not make it. It is also possible that the future's version of electronic money will be called BitCoin (it's just a trademark), and work differently than today, maybe even backed by all the worlds governments.
Who knows.
Crypto-currencies have a future, Bitcoin probably not because of its finite amount and the inevitable upstart that will out perform it.
Even if crypto-currencies fluctuate so much, represent security risk and aren't worth the trouble to use instead of traditional currencies, they will stay a marginal phenomenon useful to criminals and people who fear guberment. The cat is out of the bag now, but a marginale cat. Unless for some reason a lot of people decide to use them to avoid sell taxes and enough employers adopt them to pay their employees.
There is a very subversive element to crypto-currencies that elites who label them as useless gimmicks do not understand. If governments are not capable of collecting revenues they can't function and that creates another boatload of problems.