Actually, I think the big problem that exchanges will come up against is anti money laundering rules - specifically so called 'know your customer' rules. Truly anonymous bank accounts aren't permitted - the bank (or in this case exchange) is supposed to know who you are.
not just that ...
who you are includes a lot more thesedays
first name /surname /middle names /previous names /maiden names
date of birth , social security,national insurance number /copy of your passport or driving licence if they can
also your address /previous addresses
job/work history from the last few years ,5 i think in the uk
income
savings
properties
investments
inheritance etc
any other cash you get from anywhere outside what you can prove is open to investigation
gone are the days of just having a "shitload of cash " and no explaination for it .....
EVERYTHING is under scrutiny thesedays