They absolutely _can_ lend out more than they take in. They tend not to because their owners are risk adverse and depositors get precedence in receivership. But you can find banks with 6 or 7 to 1 LTD (I’d not want to be invested in one).

You bother with deposits for a few reasons a) banks get a lot of power assuming they’ll play a public good in the form of managing deposits and b) they can earn more using the deposits than they have to pay out to depositors.

Nope. Pretend I’m a bank with no assets and no debt, and I give you a loan for $100.

I then have $100 in assets and $100 in liabilities.

When you withdraw the $100 loan, I borrow from another bank or from the central bank, and give you that money.

I collect deposits because it’s a cheap source of liquidity.

Critically, your asset is the loan, the liability is the deposit credit in the borrowers account but you have zero liquidity and are actually done for when they ask for the money.

So you either need to borrow the money from another entity (if perhaps you were better at loan origination) ahead of that, or more likely use owner equity to payout the loan.

Which is where the capital that is required to create the bank comes in, since that provides the initial (cash) liquidity.

This is the classic description found in the economic textbooks. Unfortunately it is incorrect, the system doesn't work that way. (See comments above).

apropos btw. I've never actually seen a banking system that has a 10% ratio, I think that was Keynes chosing easy numbers. The reserve ratio back in his day was more like 20-25%, these days it is down to about 1-2% in most countries, and being replaced with terms like "required liquidity ratios".