If we follow your train of thought, we shouldn't see employers paying minimum wage with higher margins because those higher margins would have transpired to lower prices for consumers.
McDonalds corporate profit margin is 20%! People might say, "Well most margin comes from franchise fees and McDonalds doesn't directly own most restaurants or own that cost base" - but while some franchisees earn 12%+ profit, they don't even have a mechanism where they are even ALLOWED to reduce prices so how exactly are higher profits supposed to get passed back as lower prices?
The reality is that if a companies goal is to profit-maximise, "cost plus margin" is not a particularly effective strategy. From an economics perspective, you would work out what your demand curve is, plot that against your cost base to produce a profit figure for each point on the demand curve, and pick where maximises profit. In reality this will be less of a formal process, but this is the microeconomic theory.
And this is not something that hasn't been tried in practice yet. Just look at European countries like the Netherlands, Belgium, Germany, France, Spain etc. They have significantly higher minimum wages (relatively to their GDP or median household income) than the US and consumer goods and services are in general much more expensive (relatively) there than in the US.