In the interests of disclosure and not as an assertion of authority: I must admit that I am a lawyer and my perspective is shaped by my dissatisfaction with the profession's lack of scientific rigor both in the academic and practical spheres.
And as an initial matter, I would point out that there is no judicial procedure which relies on algorithmic sentencing or bail decisions without a judge reviewing the decision. COMPAS is merely used to produce a recommendation for a bail amount which a judge then has to review and approve. Defendants are still afforded a hearing where they can object and raise any extenuating circumstances. So to the extent that judicial discretion can address systemic biases, it already does.
And I certainly recognize the value of judicial discretion. Mandatory minimums alone demonstrate how prioritizing the punitive and retributive goals of the judicial system over simple human mercy can amplify the negative effects of racial and other social biases.
However, my experience has been that the legal field has a strong systemic bias against empirical or statistical techniques. Essentially anything that involves math. There's a running, tired joke at every law school that students pursue JDs because they couldn't get a good score on the math GREs (the LSATs in contrast involve no math).
And to clarify since I am at risk of confusing what we mean by the term bias: I am not denying that the legal profession is susceptible to the social biases you mention, but rather I would argue those biases are impossible to address until the deeper, methodological biases in how the legal profession pursues objective truth are addressed.
Algorithmic sentencing and bail setting software can assist there in two ways. First, it ensures the collection of extensive, objective, and standardized data that can be used to evaluate the potential systemic biases you are concerned about. A single, consolidated, structured database with enormous amounts of information about each individual defendant is a gold mine for researchers. Simply put, we cannot even begin to resolve our biases without first identifying them. Software like COMPAS can help (though I'm not sure if it does in this case because I don't think they provide public access to the data).
Second, the introduction of this software gives lawyers a chance to get used to machine learning algorithms and other advanced statistical tools. They're powerful techniques and need to become a larger part of the standard lawyer's tool kit.
I don't think COMPAS is the terminal destination for sentencing software. In fact, I really hope otherwise. But, as a profession, I think we need to start taking steps to modernize our practices, one little step at a time. Each individual step may be imperfect at first, but so long as we maintain judicial discretion and careful oversight, these tools will be a boon for American justice.
And in response to your last question, I don't have a citation on hand. I've read it somewhere before. Basically they replace a professional clerk or low level prosecutor in the DA's office who prepares a bunch of data and biographical information for the bail recommendation to the judge. It ends up being about one FTE a year and the software costs less than that to license.