Morton was initially arrested and convicted of the 1986 murder of his wife. At the time, DNA testing was not advanced enough to be used as evidence, thus discovering this evidence
One shocking aspect of the case is that his lawyers sought to have the DNA testing done for six years before it happened. Also, Morton's son, who was three years old at the time and witnessed the crime, told his grandmother that a "monster"
So it seems the justice system is working to correct the wrong done at some level, but why did this even happen in the first place? Aren't there laws about the prosecution sharing with the defense all the facts they find? Yes, there are; they are called discovery laws. According to another Texas Tribune article ("Morton Case Sparks Calls for Texas Evidence Law Reform") the US Supeme Court decision Brady v. Maryland requires prosecutors to provide defendants with "exculpatory evidence," meaning any information that could prove that they are innocent. The problem is that the state of Texas does not have an official definition of "exculpatory evidence," so the interpretation of this phrase is usually left up to trial judges or prosecutors. The state does not even mandate basic information sharing such as police reports. Even so, many district attorneys in Texas have mandated that their lawyers share information with the defense. In the end, some prosecutors in Texas have no obligation to share much information at all.
Why hasn't it been fixed? Well, since 2007, legislators have proposed more than a half-dozen measures that would have expanded access to discovery, but none of them passed, largely blocked by legislators. The article above ("Morton Case Sparks Calls for Texas Evidence Law Reform") explains the motivation behind uncooperative prosecutors by interviewing Sen. Rodney Ellis (who is a lawyer). He says, “The role of the prosecutor is to discover the truth. But oftentimes there’s more interest in getting a conviction.” He goes on to say that many Texas prosecutors view a conviction as a win.
So is the Texas justice system broken? I would say that, as we see in the case of Micheal Morton, the system does function, but must be reformed in this area to prevent any further injustice. The laws about discovery must be revised so that there is a clear standard of what is "exculpatory evidence," and legislators might consider enacting further laws that ensure all the facts are presented.