yes, the entire reason a bank is needed in all online transactions is because nobody trusts YOU to not double spend, but they do trust the bank to make sure they don't let you spend your money twice.

Then the banks have solved the double-spending problem, so in effect there isn't one.

I was asking the question because if double-spending has been solved, then why do we need crypto/blockchain?

Sure, if double-spending has been solved for you, you don't need a blockchain. It hasn't been solved for everyone yet though. A great book to learn about this is: Check Your Financial Privilege (https://www.amazon.com/Check-Your-Financial-Privilege-Gladst...)