I understand that cutting of the money supply for terrorist is very effective, and I can understand bitcoin as it can move large amounts of money
Also, you need to understand that the main keypoint of bitcoin: is that it's distributed.
Bitcoin protocol advantage isn't that you can move these large amounts of money anonymously.
Bitcoin protocol advantage is that it's only the poeple involved that get to make the call, there's no central authority.
This lack of central authority is done by the distribution. Every single transaction is broadcast to the whole network, and is stored into the blockchain: a huge virtual ledger of which every single node in the network has local copy. That's far from anonymous. That's publicly broadcast.
The bitcoin protocol still provides pseudonymity. In the blockchain, transaction aren't stored together with some username/identity. There is none as there's no central authority with which to register. Instead in the blockchain, transaction are signed with cryptographic key. And each user's wallet generates constantly new cryptographic keys specific to this user.
For an individual, it might not be easy to track every single such use of cryptographic key, in order to be able to trace a "money trail" between 2 users on the network.
But for a government, even more for an entity as the whole european union, that's well within their capability of "Big Data" analysis.
Much more easy to track than plain cash: with plain cash, you only get to read the serial number when the ATM handle out the money at one end of the chain, and when the deposit machine gets the cash back later. Any transaction that has happened in between is left to the imagination of the detective.
Whereas with bitcoin, it's as if every single movement of cash note was publicly broadcast. Be it when the cash changes hands (e.g.: an actual transaction between a merchant and a seller) or simply changes pocket (metaphorically symbolising the constant stream of generated crypto key as part as the normal function of a wallet).
A single individual might not follow it.
But a government could at least do the tracking, alghouth they can't block it (that's the whole point of the "no central authority").
Also, law is still law, and all the law against money laundering still apply against any institution that handles money. No matter if the money is plain cash, or credit cards or, in this case a weird protocole with no central authority.
BTC exchange, payment processor, etc. all requires user registration, and all require all the other procedures in place against laundering.
Simply, the transactions happening bitcoin will happen without any control from 3rd party (just like cash changing hands, although better traceable, as mentionned above).
Unlike transaction with credit card and central payment processor like Pay-pal, where the Visa, MasterCard or Paypal companies are able to freeze accounts and reverse transactions.
Bitcoin protocole still offers advantage for the average citizen: absence of monopoly.
(mainly the main advantage of cash, except that it also works online.
or the main advantage of SEPA payment, except that it works anywhere in the world, not only between european bank account supporting the protocol and a faster speed being minute to hours instead of next-day to days)
- freedom to chose one provider and interact as long as everbody else supports the same protocole.
- not a single company being jury judge and executionner (like with credit card companies and charge-backs), but instead enabling complexe multi-party scheme, were seller and buyer can freely agree before hand on a 3rd party arbiter (a role that the various consumer associations and certification groups in europe would be happy to play)
- not being at the whim of Visa/MasterCard freezing acount. Currently it's not possible to use a Credit Card to pay anything that they don't like.
(e.g.: you can't donate money to whistleblower. Wikileaks got their account frozen. In fact bitcoin was started in the reaction of such incidents)
in fact anything that is perfectly legal in your jurisdiction and culturally accepted in your society, but is disliked where the payment processor happens to be headquartered, is at whim of being frozen.
Such things are impossible with bitcoin protocol. There's no central authority that can prevent of freeze them. Only local law apply locally to buyer / seller. (Meaning if selling weapons is illegal or heavily regulated in your jurisdiciton, police is going to whatch you, even if you don't use credit card to charge your customer).