This reminds me a little of the breakup of the Atomic Energy Commission. The AEC was supposed regulate and promote nuclear energy. This conflict of interest was recognized in the 70s and it was split into the Nuclear Regulatory Commission and ERDA (which soon became the DOE).
In 1971, the National Association of Securities Dealers (NASD) gave birth to NASDAQ, which became publicly traded in 2000, and then a national securities exchange in 2006. NASDAQ wasn't really independent of NASD until 2000, so for a while the same people who owned the exchange also regulated it.
The NYSE is much older and became a Not-for-Profit in 1971. In 2006 it merged with ArcaEx and became a publicly owned for-profit, later merging with Euronext in 2007 and acquiring AMEX in 2008.
Here's the weird thing: exchanges are supposed to self-regulate, with the SEC basically just approving the rules they make for themselves. And the exchanges kind of 'outsource' their regulation - but not all of it - and that's not all that well defined anyway.
In 2007, NASD's and NYSE's regulatory and enforcement committees were merged into a new organization, FINRA, which basically makes the rules their members are supposed to abide by and enforces them in coordination with the SEC.
The SEC has been investigating exchanges since the "flash crash" of 2010, when it was shown how completely fragile the market had become by large players making very large trades, as well as new high-frequency automated trading.
In 2011, NYSE Euronext tried to merge with Deutsche Börse, which would have become the largest stock market in the world by far. It actually passed US antitrust investigation. But in 2012 the European Commission blocked the merger as it would have created a 93% monopoly on European derivatives trading. This doesn't have anything to do with the exchanges violating rules, but it does show how without regulation, monopolies would be a virtual certainty.
In 2012 NYSE was fined 5 million for giving data to its customers before the public. In 2014 NYSE was fined 4.5 million when it was found to have violated its own rules, or lacked rules it should have had.
Compare this to NASDAQ settling with the SEC for 10 million just for mishandling Facebook's IPO in 2013. This is apparently because the SEC stopped short of finding the NYSE's actions as felonies. And all of this is relatively new, as exchanges historically were never legally scrutinized or punished for their actions. (Their revenue is in the billions, so these fines are basically just for show)