• It's not means-tested. It's available to (nearly all) citizens. Exceptions include some workers classified under the Railroad Retirement Act, and the self-employed.
• It's funded from taxes assessed over your working life. Actually, BI would likely take this one step further, as there's an income cap to SSI contributions. Lifting that cap would make SSI more BI-like.
As to the rest of your points: with universal healthcare, you'd eliminate the need for means-tested medical assistance. With universal higher education, you'd eliminate PELL Grants (already pretty limited -- most college financial aid is now in the form of loans, with their own class of problems). BI would directly address the goals of welfare and food stamps, and EITC is effectively BI in limited dress.
I'd be open for programs which do address specific remaining needs: say, treating drug addiction as a public health, not a criminal, problem (though drugs trafficking might still fall under the latter in cases), and other programs addressing those with specific needs (health, disability, etc.). But yes, you'd be wiping out a large class of present means-tested programs.