David Brooks claims that mandatory minimums have nothing to do with mass incarceration, but he misses the fact that mandatory minimums and prosecutor behavior go together. Over 95% of criminal cases are "resolved" without trial. Prosecutors use the threat of harsh mandatory minimums to coerce guilty pleas from defendants. Underfunded public defenders know that they won't have the resources to give their clients an adequate defense, so they encourage their clients to plead to lesser charges.
A couple weeks ago, a case exactly like this made national news. A teenager in North Carolina was charged as an adult felon for taking a nude selfie and sending it to his girlfriend. This caused a bit of outcry, which faded when he pled guilty to misdemeanor charges. What everyone seemed to miss is that the prosecutor never cared whether he could get a conviction on the felony charges, and probably didn't want to go to trial. The prosecutor wanted to raise the stakes for the defendant, so that the defendant would waive his fifth amendment rights and plead guilty.
It worked, and we were all happy with that.