> I think people would be outraged if someone told them it belonged to the bank.

You might find it interesting to read about 2013 Cyprus bank levy then. The government unilaterally raided people's savings accounts, taking between 6.75% and 10% as a one-off tax with essentially no warning. When you put money in the bank you are implicitly accepting the (small but real) risk that the government will come along and say "I'm having some of that" and there's nothing you can do about it.

More anecdotally, I once had to help a family friend sue a bank for several tens of thousands of pounds in the UK because they refused to pay him back his balance when he closed the account and refused to explain the reason. It took a little over 6 months to get the money back. While researching the case, I discovered countless other cases in which businesses had gone bankrupt because of delays in recovering their money from the bank. Under UK legislation, banks can and do do this if they have "suspicions" of money laundering (which can be triggered for any reason whatsoever - the suspicion doesn't have to be reasonable). Not only do they not have to explain to the customer what those suspicious are, they are legally required not to. They can hold onto your money for up to 31 days and this can be extended to up to 6 months by a court order after a hearing which you will be excluded from and likely not even know took place until after the fact.

Legally you do not own your money in the bank. Instead you own a "chose in action" (https://en.wikipedia.org/wiki/Chose) which is the right to sue the bank for the money. Although it sounds similar to outright ownership, it's not the same thing.