I agree with (2) but on (1), isn't that about the liquidity _of the bank_. And when banks are illiquid like they were in 2008, the central bank creates liquidi

I agree with (2) but on (1), isn't that about the liquidity _of the bank_. And when banks are illiquid like they were in 2008, the central bank creates liquidity through QE which isn't a bad thing unless you are questioning these banks' ability to repay the money they "borrowed" from the central bank.