The intent of the lawmakers doesn't matter. The law allows you (or the child) to use the Social Security money for whatever you want. Using a loophole (if that's what it is) is perfectly legal. It's not an evasion.
Anyway, as Hal_Al said, based on your figures it appears that even if you use all of the Social Security for basic expenses the child is not providing anywhere near half of his or her own support. So there is no problem claiming them as dependents and using them to qualify for head of household filing status.
Stop worrying.
