I find it really strange that it happens that so many Bitcoin exchanges have their bank accounts closed.
Outside of the Bitcoin world, I find it very unusual to have a bank account closed, for a reason other then inactivity. The only case I remember is Julian Assange's Swiss Postfinance.ch account closed.
Maybe its a specific practice of banks in certain countries?
Many banks that I had been dealing with, seemed to have the attitude that everyone with a passport (for individuals) or company papers (for companies) can just open an account, no matter what is his business, if he is trading spaghetti, sand on the beach, air or voucher codes is none of banks business, they only worry is that the person who opens the account is really the one who he says he is. The bank doesn't have to understand your business, their business is to verify ID and do maths. The rest is the customers business and responsibility. Of course the bank has to report transactions over a certain threshold and/or suspicious to a certain government agency, but closing accounts?
Maybe its the matter of attitude, common practices, banking culture being different in those countries that the banks closing the accounts where established? The Bitcoin exchanges accounts closed where mostly in "old" western EU (UK, France), and the much more relaxed "no bullshit" attitudes of banks I have encountered is mostly from Central/Eastern EU banks ("new" EU countries).
Is it common for western EU banks to be so picky about customers, and closing accounts despite meeting formal ID requirements of the companies?
The sometimes mentioned claim that it might be illegal to "hold other people's money if you are not licensed to do it" is not very plausible, as any business "holds other people's money" for some time, and they are even ones which sell "numbers which hold a value" for money - prepaid vouchers for mobile phone recharges for example. That voucher is usually a 16-digit long number that holds some value - if that is fine, then Bitcoin must be no different - both are basically selling numbers which hold monetary value.