Technically true. But the minimum wage is still clearly an anchor. The amount above minimum is a signal of your worth as a worker. Consider this[1] income distribution chart (with its precipitous falloff left of the minimum wage mark). It's clear that "at or just above minimum" is the largest demographic, even if it represents a small fraction of the whole. If the minimum wage were raised, it wouldn't simply bunch the left of the graph together - the entire curve would move.
Of course the entire curve will move, but then inflation will just go up a similar amount. This means that everyone will effectively be making the same amount of money.
Because of this, I think minimum wage is unnecessary and just manages to distort the market and prices out some people out of any job whatsoever.
[1] https://upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Di...