But would it have been better to let the banks fail? (Serious question)
Economies require a functioning banking systems. Banks represent one part of the transmission mechanism that lies between the Central Bank and the Real economy. So there is a key distinction between letting one bank fail (Barings) and seeing a systemic failure of the whole banking system. Arguably Lehmans lay right on the boundary of this distinction!
So the answer, it depends on the risk to the whole system and to the economy.
BTW, this is still a problem as banks are failing to provide this transmission mechanism now which is why the current policy mix isn’t working, But that’s another issue related to fact that people don’t understand the nature of the current slowdown.
Being able to get to a point where something is too big to fail (regardless of the discussion about whether state rescue should happen) is a problem with capitalism though, isn’t it?
No, it is a problem of excess leverage (part of which has been encouraged/driven by the heavy hand of the state and central bankers resulting in markets that are anything but free. )