>There's also a fairness (and rule-of-law) argument: if two people steal $100 each, why would one person be let out earlier?

If that's your justification then the horse has already left the barn, developed space travel and colonized Mars. Look at the number of factors that go into sentencing -- or just the definition of the crime, like what was stolen (distinct from its market value) and how (e.g. on a computer vs. in person vs. in a conspiracy with accomplices), then there is a lot of flexibility for the sentence itself (most sentences are "up to" X penalty) with a whole list of mitigating and exacerbating circumstances in the sentencing guidelines, subsequent parole for good behavior in prison, etc. etc.

I wasn't justifying anything. The person to whom I replied ignored a few obvious and valid arguments, and I was filling that void.

Even if prison was entirely intended for corrections, it is punishment (a denial of freedom). So there is a fairness argument that if two people do reasonably similar crimes that they should get comparable sentences. That is just one argument though, and fairness (as always) is weighed against other arguments.