So, most US businesses pay wages equal to the minimum wage, plus some fixed "bonus" salary ?
wage = minimum + ($X per hour)
If so, then the minimum wage has become a "benchmark wage", affecting the entire labor market, or at least the entire "low pay labor market", of all jobs within a few dollars per hour of the minimum. If so, then now i understand what you are arguing. Never-the-less, that would only
amplify the impact of raising the minimum wage. Instead of increasing minimum wages only eliminating jobs
at minimum wage, jobs even
near minimum wage would also be eliminated.
Psychologically, the word "minimum" is derogatory. Workers earning "minimum" wage may feel intrinsically denigrated, instead of understanding, that they are working for (current) fair market wages. If a box of cereal is only worth $1, then must it be a "bad box of bad cereal"? No, prices are set by market forces, of supply & demand.
Eliminating the minimum wage would re-authorize millions of low-pay jobs, and (possibly) reduce wages for those working near minimum wage today. But, without
any benchmark wage to refer to, why would employers suddenly decrease wages? And, employing millions of Americans would reduce competition, for all other jobs, tending to
increase wages?