Banks don't lend out deposits. They don't take deposits and lend out 90% or so. Fractional reserve banking is a model of how banking works but it's a wrong model. In reality banks make loans (which create deposits). They try to attract deposits from other banks because they need enough bank reserves to cover liquidity issues (like customers transferring money to other banks). When a bank transfers deposits to another bank, they must transfer reserves too. There is really a 2 tiered money system in the US. There are bank reserves (which you and I can't have) and deposits (which you and I do have).
> Fractional reserve banking is a model of how banking works but it's a wrong model. [...] They try to attract deposits from other banks because they need enough bank reserves
Ultimately it's the capital that the banks have that limit how much they can lend, not reserves. Their capital requirements are the limit. Once capital falls below a certain percentage, the bank is in trouble.
How banks actually work was described well by the Bank of England. https://www.bankofengland.co.uk/quarterly-bulletin/2014/q1/m...