Setting aside any specific mechanism, the overall point still seems plausible. Assuming we can prevent the primary causes of aging (e.g. telomer shortening), we

Setting aside any specific mechanism, the overall point still seems plausible. Assuming we can prevent the primary causes of aging (e.g. telomer shortening), we will likely start to find other parts of human biology that start to fail, either because of additional aging mechanisms, or just limitations of the body's self-repair mechanisms. Human biology is incredibly complex, and there has been no evolutionary pressure for it to sustain itself beyond its natural biological clock. These problems are probably solvable eventually, but not until we live long enough to see them. Which problems means we will have at least a few generations of people die after the initial old-age cure.