The big thing traditional institutions give you is logs of everything. Sure if I get your account number I can take all your money - but there are traces of that and so it is easy to arrest me after the fact.

Don't give out your account numbers, there will be a lot of hassle should an evil person get it. However you have a reasonable change of getting your money back in a couple years. (this is also why you get warning about some countries - a few will not cooperate with traces and so the money is lost)