I think it's Bobby Doerr. The longevity of his signing window is unmatched; he broke into professional baseball in 1934 and likely started getting autograph requests around then (or at the latest, his MLB debut in 1937), then kept signing until a couple weeks before he died in 2017. He never charged a fee either; even the nominal one charged by many of the others mentioned would have cut down on requests to them.
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Signed 1953 Topps set: 264/274 (96.35 %)
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