I would argue the following.

If banks have negative economic externalities, such as causing boom and bust cycles, and such as causing large-scale economic disruption when failing; then you cannot consistently believe in libertarian principles, while also being in favor of banks.

I have described previously how banks are inherently volatile and prone to collapse based on rumors alone - unless their depositors are insured with a system, such as the Federal Reserve, which can print money freely.

On the other hand, if banks and bank-like institutions are protected like this, then they require regulation to avoid moral hazard leading to exploitation of the money printing facility.

The stability of banks thus inherently goes hand in hand, not only with big government, but big government with the ability to print money freely.

I suppose that, to libertarians, this should be anathema. There is no greater power in the world than to have hundreds of millions rely on your currency, while you have the ability to print it freely. Meanwhile, the marriage of government regulation and banking that is required for banks to be stable, limits competition and encourages the development of a few behemoths who monopolize the banking market - and, by extension, play a vastly (too) powerful economic role. Perhaps leading to an even greater chance of systematic failure.

Libertarian policy calls for a small and effective government that operates based on a few robust principles. These might be:
  • Rule of law.
  • Respect for property.
  • Using coercion only to prevent coercion.
Note that these principles are all reactive. A libertarian small government does not manage the economy. Such a small government is not proactive. It is simply a guardian of people's rights. Such a government only acts when called upon for: when an individual's rights are threatened, or when a dispute needs to be decided upon.

For reasons of principle, a libertarian government cannot get involved in regulating the financial sector, for instance. That would be 'managing' the economy. Instead, the following two states of the world are consistent:
  1. Banks are permitted, but not backed by the government. They frequently fail, often merely based on rumor alone. Depositors lose money, and might therefore consider things more thoroughly next time. But no one else is harmed. Wiser people spread advice that banking is a form of gambling, and that the interest you receive on your account is largely offset by the likelihood that the bank will fail. Unwise people continue to make bank deposits, and periodically lose money, but negative externalities for uninvolved parties are small.
  2. Or, perhaps, it is found that banks do indeed cause substantial negative externalities by causing boom and bust cycles and by spreading a systemic risk of failure. In this case, the libertarian government must react to prevent negative externalities on the uninvolved, and therefore prohibits fractional reserve banking. All loans are thus required to be credited with money explicitly provided for the full duration of the loan.
So: either fractional reserve banking doesn't truly have negative externalities, such as boom and bust cycles and spreading of systemic risks; or else, a libertarian government should prohibit fractional reserve banking.

Is there any third option?