Apparently the Fed does not allow the operation of full-reserve (as opposed to fractional-reserve) banks:

> Some banks, such as TNB Inc. and others, have attempted to make bank models that just store all of their assets as cash at the Federal Reserve and therefore operate full-reserve banks, but they have not been allowed by the Federal Reserve to exist. This would basically be the safest possible bank, but if it were allowed to exist it could suck deposits out from other banks, threaten the whole fractional-reserve banking model, and reduce the Federal Reserve’s ability to control monetary policy.