Why does the government need to control interest rates? Context
As far as I understand, economic cycles are mostly dependent on the amount of demand (which is influenced by money supply, which is in turn influenced by the availability of credit). Since credit dwarfs cash as a % of total currency, credit is by far the most important driver of money supply. 
In general, the government controls interest rates to slow down an overheating economy, or to expand a slowing economy.

Question
My question is, why do we need government to control interest rates? Assuming banks are rational and want to make money, wouldn't banks tighten credit rules in the midst of an overheating economy? If banks sense that debts are too high, wouldn't it make sense for them to increase interest, or stop lending to risky customers to avoid customers that default on their debts? I don't see why government is any more qualified at controlling interest rates than banks themselves. You could argue that banks are greedy, but at the same time, they're smart and have a long-term view. If a bank loaned money in an overheating market, they wouldn't be in business for too long.

Thanks!
why do we need government to control interest rates? Assuming banks
  are rational and want to make money, wouldn't banks tighten credit
  rules in the midst of an overheating economy?


I assume that by government you mean central bank. Otherwise, I agree with you by saying that governmental intrusion in monetary policy often creates inefficiencies and distortions.

The purpose of any [private] financial entity is to maximize its profits rather than the stability of the domestic currency. Thus, a central bank's primary goal is (or should be) to procure that currency stability, which it pursues by "printing money" and issuing bonds. The conventional term "control [of interest rates]", however, is a overstatement/misnomer from the standpoint that financial entities are not prohibited to transact with each other (or with the public) at lower or higher rates than the ones pursued by the central bank.

That being said, a central bank's pursuit of other goals in addition to --or in lieu of-- currency stability tends to impair its ability to achieve that primary goal (see also last paragraph of this answer). See, for instance, the Federal Reserve's assertions of its dual mandate of maximum employment and price stability. Notwithstanding Ben Bernanke's renown inflationary profile, his repeated calls in the midst of the Great Recession for Congress to enact reforms reflects his awareness that his monetary policy of essentially printing more money was improper, insufficient, and/or ineffective to address the core issues of the labor market. The vulnerability is more severe in those economies where a government exerts greater control on that nation's central bank.


  You could argue that banks are greedy, but at the same time, they're
  smart and have a long-term view. If a bank loaned money in an
  overheating market, they wouldn't be in business for too long.


Some financial institutions negligently or recklessly incur excessive risk, thereby causing severe repercussions when unexpected market conditions occur. Consider the Barings Bank. This entity was founded in the XVIII century, yet the lack of scrutiny of a strategy performed by one of its hitherto "star traders" caused its collapse in 1995.

My allusion to the Barings Bank diverts from your central inquiry, but it illustrates that an entity's longstanding prevalence in the economy does not disprove the necessity for a [purportedly disinterested] regulator or central bank to scrutinize anomalies that are potentially catastrophic.