First off, prison labor hasn't been phased-out in the United States, quite the contrary; it's at an all-time high. For example, Microsoft's boxed software is assembled by prison labor in the United States. The primary reason why State governments were reluctant to permit prison labor wasn't fear from the left: it was fear from unskilled labor voters who didn't want their jobs taken from them by prisoners. It wasn't until our workforce became better educated that prison labor began to be accepted, as it was no longer seen as something that was taking jobs away from law-abiding citizens. This is also why labor is used in many privately operated prisons: they don't have to answer to voters.
Secondly, three-strikes laws have proven to be completely effete at combating non-violent crime. Drug possession charges, which have seen the widest adoption of three-strike laws, have tripled since 1982. Meanwhile, violent crime has dropped steadily and is currently at the lowest rate we've seen since the 1960s (this despite the fact that the death penalty is applied less and less).
Regardless, three-strike laws are unsustainable long-term, as State governments will be forced to pour far too much cash into prisons, putting them in a position to either raise taxes, or cut services - two very dangerous political propositions.