On the surface, the pro side seems absurd and extreme, but in-depth research has proposed many reasons and solutions for the premise. Remember that the topic says "Should", so even if it was impossible to fully accomplish, pro may still win on a theoretical aspect (Ex. "we SHOULD aim for perfection", "we SHOULD strive for equality")
I. Inflation Issue
In the words of Rahn, chairman of the Institute for Global Economic Growth, "
the current Fed policy of ultralow interest rates of less than 1 percent for banks and money‐market funds, combined with high inflation rates of 3.9 percent for the past year, is a formula for a new disaster. If a saver can only obtain 1 percent or so on cash savings but inflation is running at almost 4 percent, then the saver is losing 3 percent of his money each year in an inflation tax".  He supports this further with statistics, "The U.S. dollar, for instance, is now worth only 1/22 of what is was worth
when the Fed was formed in 1913, and most other central banks have even a worse track record." But the Federal Reserve is contradictory with its set premises. It intended usually for only 2% of inflation rate, which has been clearly failed in data
. Murray Rothbard had his famous support for abolishing the Federal Reserve and central banks, and there will no longer be lenders or the bailouts which trouble the economy.
Consider the original purpose of the Central Bank. Alexander Hamilton intended to boost the imperialism and the warring ability of the US, even at the cost of the debt. And look at where we're at now. Trillions of dollars within debt, and no necessity for war to be conducted. He refused the trading and economic boosting logic of interacting with other nations, instead, trying to focus on our own independence. But the printing of the dollar was commonly known to cause a big bust
, the Great Depression, the most famous economic decline of all time. This is non-unique to the US and had occurred in Germany, Zimbabwe, among other countries.
In fact, this inflation issue is most worrisome for developing countries. With problems occurring with exchange rates, none of the Central Banking systems have succeeded. A news article admits, "Developing countries established central, banks with high hopes that have been unfulfilled. The best thing they can do to reverse their poor monetary and economic performance of recent years is to abolish their discretionary central banks and fix their currencies to foreign currencies with relatively good records of low inflation. The currency board system is a well understood and eminently practical way of doing so. Other alternatives to central banking are also worth considering. The important thing is to minimize, and preferably eliminate, discretionary government control in monetary policy."  As you can see, Central Banks' implementation have failed time and time again.
II. The Power Problem
Friedman is a famous economist who also noted how Federal Reserve was the main problem that caused the Depression. With the actual practicality of ridding of Central Banks being a problem, he proposes a way which this may be accomplished. "Friedman was in favor of abolishing the Federal Reserve System and replacing it with a mathematical model that would keep the quantity of money increasing at a steady rate, issued directly by the government (Treasury) and ending fractional reserve banking powers for the banks, which is why he supported our Monetary Reform Act. He said he actually would “like to abolish the Fed“, and pointed out that when he wrote about reforming the Fed it was simply his recommendations of how it should be run given that it exists."  It's not impractical, nor impossible for Friedman's proposal to succeed; putting the money directly in the hands of the actual resource for money is more logical than giving control of the bank which the citizens have very little say over.
Of course, Friedman received controversy over his seeming pure view of capitalism. Some regulations are definitively necessary, for monopolies and retaining law and order. But the Central Bank is a more specific purpose that misses out on its actual impact and need to keep its implementation. The Federal Reserve, being controlled by only a dozen or so people,  despite being so incredibly powerful, brings questions about its checks and balances. The President himself picks these people, which means that he potentially has greater influence over the central economic system. Sure, the people pick the president, but given the lack of other controls (what if they are biased? How can you get rid of them?) this sole source of power is problematic.
Connecting back together to point I, the economic control with unlimited reserve combines together to give an enormous amount of ability to change laws, despite not specified in Constitution. Charles Plosser, former president of the Federal Reserve Bank of Philadelphia, had stated: “A large balance sheet unconstrained by monetary policy is ripe for abuse. Congress and an administration would be tempted to look to the balance sheet for their own purposes, including credit policy and off‐budget fiscal policy.”  It's difficult to say that mere reformation alone would be enough to prevent Congress to abuse the power and use of the Federal Reserves. The extra spending out of deficit is definitely dangerous in the long run.
Combined with the inflation influencing the poor from point I, the disposable income reduction is further destroyed with the fact that Federal Reserve Benefits Special Interests
for the most part. Business Insider has noted that big bank bailouts have amounted to nearly $16 trillion over the years, an astonishing amount.  There has been famous lobbies by these groups, highlighting its power even over Congress itself.  The bias towards rich and powerful people causes the inequality to widen, which has greatly negative implications. One research article says: "In particular, when inequalities become persistent and some groups are systematicallybarred from the benefits of growth, the economic and social costs are likely to intensify asthose at the bottom claim their share of the national income by any means possible, thuscreating a more unstable macroeconomic environment."  It is also widely known that widening inequality results in greater health and social problems
, which is already looking bad with US's wide disparity between the richest and the poorest. The big problem is that the Central Banks currently favor the rich
(inequality is not viewed as a primary concern), and this can't be fixed due to the biases of the bank. The monetary policies are near impossible to implement, and the fact is that most of the powerful people with way say will want to keep their money income, making it implausible to fix this inequality without abolishing the central bank.
Conclusion: The Federal Reserve has been tried true and with countless reformations attempted. The only reason it's still here is that legislators can't agree to abolish it. But in an idealized world, we should abolish Central Banks. They do nothing but hurt the economy and increase wealth disparity, while holding too much power over finances.