Killer app for Bitcoin is Bitcoin itself. Digital gold that can't be easily confiscated, can be cheaply stored and transferred and resist a lot of censorship.
1. It's easier to hide even the fact that you have some Bitcoins. When you buy some Bitcoins for cash from random people on the street and keep in different wallets (or even "brain wallets"), no one would know how much do you have. In case of Swiss or any banking account, there's always a paper trace somewhere. And recently US was cooperating with Swiss to uncover all accounts belonging to US citizens.
2. Even if someone knows that you have some bitcoins, they don't know where they are stored and how keys are encrypted. "Civil forfeiture" or "freezing account" are very cheap and are used a lot. Irrelevant against Bitcoin savings.
3. Legal force is more costly than "civil forfeiture", but then you can always multiple ways to preserve the money: by sending it to someone else you trust, by locking it up in multisig transaction with someone you trust (who is outside jurisdiction), by saying "my hard drive has crashed" etc.
In other words, the cost for anyone to confiscate your coins is much higher than with paper cash and even higher than with bank accounts.
"It's easier to hide even the fact that you have some Bitcoins. When you buy some Bitcoins for cash from random people on the street and keep in different wallets (or even "brain wallets"), no one would know how much do you have"
...kind of like a drug dealer who has stashes of paper money hidden in various places around his turf.
"Even if someone knows that you have some bitcoins, they don't know where they are stored"
When the police make an arrest, SOP is to take all computers, all storage devices, and then look in places where tiny storage devices might be hidden. Sure, you could have buried your Bitcoin wallet in the woods, but this is not much different from burying some paper in the woods (yes, people do this).
"locking it up in multisig transaction with someone you trust (who is outside jurisdiction), by saying "my hard drive has crashed" etc."
...so basically the old trick of trying to send your paper money out of the country? Criminals try this all the time, and the police are not deterred by it.
The reality is that if you want to hide money from the government, Bitcoin has no particular advantage over paper money -- and the fact that your transactions are broadcast to the entire network actually makes it a bit harder. In any case, you also have ignored the greatest problem with off-the-books money: taxes. You can send your Bitcoin money through all kinds of convoluted paths, and then when you get out of prison and try to spend it the IRS will just swoop in and you will be re-arrested for failing to declare your income.
Paper stashes can't be put in DarkJPEG and uploaded on Facebook or Dropbox.
I'm not arguing that it's always possible to find stuff out. I'm saying the bar is being raised much higher. Today cops don't go to thousands of people to make a "haircut" on their bank deposits. It's done with a single button click and negotiation with a couple of bankers. With bitcoin you'd have to send around policemen to every house to confiscate stuff. When there's no good justification, people will strongly oppose that.
The reality is that if you want to hide from govt and govt wants to find you, then Bitcoin does not help you much (although it's certainly more mobile than cash). But if thousands of people are hiding from govt routinely, it's much more expensive for govt to go after all of them at once. See what happens with Bittorrent. Some people get caught or threatened, while thousands of others enjoy cheap movies.
Regarding last example: you underestimate the power of good mixing. You can swap coins anonymously so that all the "tainted" coins get distributed to thousands of different hands and never go back to you anymore, while you receive thousands of little coins back, from various sources, not tainted by whatever business you was doing before.
I'm not saying hiding BTC is easy now or will ever be cheap and simple, but it's certainly possible to automate and optimise security measures a lot and there will be a lot of apps doing exactly that. Right now the cost of taxation, inflation and bailing-in is very-very low and hurts most innocent law-abiding citizens (not everyone loves how the taxes are spent, but they are easy to extract anyway). With Bitcoin, huge chunk of money can safely sit in private wallets instead of bank accounts, thus making fractional reserve banking less relevant, bail-in becomes irrelevant too. Those who wish to not declare some income have much safer way to receive/send money, than with modern banking system. Most outstanding tax-evaders will be chased and caught, but 99% may safely enjoy their own little share of global black market without worries. They already enjoy local black market when they pay in cash for lots of things, but it'll expand with Bitcoin to the whole world.
It can also encode various cool contracts that are impossible to do otherwise: http://blog.oleganza.com/post/58240549599/contracts-without-... (well, this requires a UI, but it's already supported by the network).