There aren't really any dangers to having money in a bank.

The banks (at least in most countries) are all insured so if they get robbed, you don't lose your money. It seems banks are on most governments Oh crap give them whatever they need so they don't go under list, so its highly unlikely a bank will simply shut its doors or run out of money.

The only real "danger" is how much they charge you for this "convenience" and "security"

Banks charge outrageous fees for almost everything. Depending on your plans you might be charged for using a different ATM, writing checks, exceeding a certain number of transactions in a month, having a safety deposit box, or even using a real life person teller instead of an automated system.

In addition they tend to pay extremely low interest rates for the privilege of keeping your money safe with them