The big difference here is, mandatory minimum sentencing is an aberration which is engineered from the start to create more injustice. There is a reason that in a normal case, sentencing takes the history of the individual and the circumstances of the crime into account, instead of following a rulebook saying "Theft: 5 years in prison, no early release".

Three-strike laws exist to quench the mob's appetite for blood (as public execution is sadly no longer acceptable, the mob has to settle for life sentences), and get politicians get elected on a fearmongering & repression platform. But on a humane level, it's not far removed from judicial amputations.