>when someone takes out a loan, a bank doesn't lend out depositors' money. Instead money is "created" by the bank (on behalf of the fed), and the bank needs to pay the fed interest.
Commercial banks can not create loans out of thin air during normal operation. They either have to use depositors' money or share holders' capital. In other words, bank's liabilities (e.g. user deposits) should not exceed its assets (loans to users, securities, reserves at Fed, etc.). There are games which can played with how assets worth is measured (e.g. mark-to-market vs. mark-to-maturity), but otherwise the rule must be followed by banks.
>Why can we not have a similar system for deposits? A bank takes a deposit, the fed "destroys" the money, but pays interest to the bank. When the depositor wants to withdraw their money, the fed/bank recreates the money.
When a bank receives a deposit, it has to decide what to do with it. It can either loan it to someone (either directly or by buying bonds), invest (e.g. by buying stocks), pay it as a dividend to share holders (assuming it has far more assets than liabilities), or keep it in bank's reserve account at Fed. In the later case it gets payed roughly the key interest rate. This is why rate hikes suppress inflation (at least in the near term), banks instead of deploying their capital into the economy deposit it at Fed, thus temporarily removing it from circulation. It also means that cost of loans in the wider economy rises accordingly, since banks will not loan without a sufficient premium to the Fed's rate.