Once you know that death = walker, you can plan around that. Anyone at risk of death is quarantined, and dealt with before they can turn and come back. Sure, unexpected deaths will occur, but you can still implement measures to ensure that those incidents don't cause a cascade of further deaths.
The result is that you're killing walkers at a reasonably high rate while making new walkers at a much lower rate and dying at a much lower rate. As long as the supply of humans doesn't run out before the supply of walkers does, eventually you'll eliminate more or less all "roving" walkers. Granted, there are probably a couple hundred million of them, so this will take some time (probably years, depending on how many living people exist) but they'll get there.
And given that people seem to have figured out how to build more or less walker-proof settlements, such that your major risk of walker-related death is when you're outside the walls, this all seems pretty easy, really... if not for the risk posed by other living people.
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