Not sure how they would do it but I expect every time before you make a withdrawal, you will need to submit a long list of supporting documents that require yourself to declare some statements concerning where the coins are obtained. Also they could make it mandatory for companies dealing in bitcoin to register and comply to certain guidelines. I see good and bad to it.
Thats only if you do it throught a bank. They can't stop P2P (as in person to person) direct local exchange of BTC for cash. There's always a risk of it being a trap, but if you buy from a trusted seller form LocalBitcoins nothing wrong should happen. It sucks tho, it makes adquiring Bitcoin as if you are adquiring god damn coke or something.
I can see a lot of people still getting their accounts shut down. It's happened quite a few times in the UK from what I've read on this forum.
"Do you have plans to randomly freeze accounts due to "suspicious activity" where the details are withheld from the account holders for the purposes of "security and fraud-prevention"?"
I am presently unable to answer your question ;-) however I would direct
your attention to rule 162 of the standard contractual conditions, just
under those providing various forms of indemnity, and "First Born Collateral".
I can tell you that this week I am providing a free badge to all new clients
in recognition of their contribution to GDP and the employment given to
countless numbers of otherwise unemployable fact-checkers, not to mention
the launch of my new company Badge Builders Conspiracy Inc ...
What's this about and where are you quoting it from?