Social Security's admin costs are ~.7% of the program's budget, eliminating admin overhead, means-testing, and fraud fighting won't get you many gains:
https://www.cbpp.org/research/social-security/policy-basics-...
https://www.cbpp.org/research/social-security/policy-basics-...
Also this paragraph from the linked article suggests that the 0.7% figure does not include means testing:
Indeed, universal participation and the absence of means-testing make Social Security very efficient to administer. Administrative costs amount to only 0.7 percent of annual benefits, far below the percentages for private retirement annuities. Means-testing Social Security would impose significant reporting and processing burdens on both recipients and administrators, undercutting many of those advantages while yielding little savings.