Thus the reasoning behind the "three strikes and you're out" laws which call for mandatory prison sentencing for habitual criminals.

Some will not be dissuaded from crime. The rest of us deserve to live apart from them.

That is indeed the reasoning, but there is no good evidence that 3 strike laws reduce crime.

In fact multiple studies suggest that 3 strike laws have unintended consequences like increased fatal attacks on police, and twice sentenced criminals committing more serious crimes (because they will recieve a life sentence regardless of the seriousness of the offense).

agreed, they'd probably need to be substantially higher to really enter criminal's conscious consideration to put a dent in things, and even then it might only be a small dent, if any. Especially when the motivation is something like drug addiction.