From the Office of Evaluation Sciences:
… Survey data from the National Institutes of Health-supported Health and Retirement Study suggest that less than 60 percent of individuals age 65 or older who may be eligible for SSI receive the benefit, and administrative data from SSA suggest that uptake may be substantially lower.
SSA identified over 4 million individuals age 65-80 who were potentially eligible for SSI, and sent one of four letter variations to a sub-sample of them. …Individuals were randomly assigned to receive one of four letter types or to a control condition (i.e., no targeted information about potential SSI eligibility): (1) a basic letter; (2) a letter which states the maximum benefit; (3) a letter which states that applying is simple; (4) a letter combining the maximum benefit element and the “applying is simple” element. SSA sent 100,000 of each letter variation. …Of beneficiaries who received a letter, 6.0 percent applied for SSI in the nine months after the letters were sent out, compared with 1.0 percent of beneficiaries who did not receive a letter. Similarly, 2.3 percent of beneficiaries who received a letter were awarded SSI during this time, compared with 0.5 percent of beneficiaries who did not receive a letter, an increase of 340%.
Why not do this? I'll answer my own question. Social Security can't handle the caseload it has now, much less a big jump in SSI claims.