Banking History 101: Between 1819 and 1910 in the US there was a banking crisis in every 9 years on average: The panic of 1819, 1837, 1857, 1873, 1884, 1890, 1893, 1896, 1901, 1907. Since the Fed has been established we had like what, 4 in 110 years? Any imbecile wants the 1800s back? Put it in other way, in the 30 years leading up to the Fed's birthday, there were 6 banking panics, so one in every 5 years! Also, name a real country (not Tonga or Monaco) that has no federal bank. Actually, even Tonga has a central bank. The only real country without a central bank is Panama. They don't need one because... [finish the sentence]
The Fed can't be abolished except by an Act of Congress. This is unlikely to happen for self-serving reasons of financial repression. However, it can, like many central banks, become irrelevant. That's the greater issue.