The district attorney is an elected official, to the best of my knowledge, in all jurisdictions. That is what creates his or her accountability. If we are not pleased with what a prosecutor does or does not do, we can simply not vote for that person again. We elect the district attorney with the understanding that he or she is going to use prosecutorial discretion, which includes passing judgment on the decisions of all the attorneys working for the district attorney. Very few lay people have a clue what it takes to successfully prosecute a criminal case, what evidence is available, what evidence may or may not be admissible, or whether there would be a viable plea bargain option to save the taxpayers' money. If people can substitute their judgment for that of the district attorney, few people would ever run for this office. If the prosecutor must justify every action to the public, this is exactly what would happen.
Similarly, we afford the police discretion to arrest or not arrest someone, and if it were otherwise, with the public weighing in and demanding an explanation for every failure to arrest, very few people would be willing to be police officers, either.
We are all far too much the victims of the tyranny of polling, as is evident in this presidential year. Once we open the door to the this sort of thing, requiring a prosecutor to explain his or her actions, a logical step would be to have the public vote on whether or not someone should be prosecuted. This takes us back to the Romans, where the audience voted with thumbs up or thumbs down on the death penalty of the coliseum. This might seem like an exaggeration, but, really, there ought to be limits to the power of public opinion, particularly when that public opinion is so terribly uninformed.