While the sentencing may be mandatory, the charges are not. A prosectuor may choose a lesser charge, either because it is easier to make a case or to avoid a mandatory sentence. Then there is plea bargaining, which definitely is subjective.
No. Quite the contrary. Consider mandatory sentencing for a given crime that a legislature might enact -- that's a clear violation of the separation of powers between the Legislative and Judicial branches of government. In this case, there's no discretion by the Judiciary, since its sentencing decisions have been codified into law by the legislature.
At first blush it appears just to have sentencing guidelines, that those who are found guilty of a specific crime should be punished similarly. However, the power of the Judiciary should be that it assesses as much information relative to the crime as possible, and have the punishment fit the crime. The crime of "Stealing Bread" might carry the same punishment, but the punishment should be different if a perpetrator steals one loaf to feed his or her children, as oopposed to a perpetrator who steals bread every day as part of a "bread ring" which then fences the goods and splits the profits.
Discretion is necessary for the Judiciary to function properly.
Are you refering to subjectivity, or the "human" element? If so, the system was designed to contain a healthy combination of both subjectivity and objectivity. For instance, though subjectively we might consider someone's past when we consider guilt, in the courtroom, such evidence is usually not allowed, because it is too prejudicial. We have juries who are always subject to their own biases, yet the are instructed as to what evidence to consider and which to ignore. Even judges, who are given wide discretion in adjudicating a case, are subject to recusal and having decisions questioned an overturned by others. This "balance" sometimes swings in one direction or another, but, for the most part, it works far better than any other sytem we know of.