It's easy to see the logical flaw here by considering a reduction to absurdity. Imagine a minimum wage of $200/hour. This would of course lead to mass unemployment and collapse the market, except for a very minuscule percent of the labor force in extremely high skill high value positions. Just because somebody would now be earning $200/hour most certainly would not mean they were not valued. Instead you'd have simply squeezed everybody out of the market except these most incredibly valuable employees.
But you can also see the same flaw by just considering a mathematical distribution of wages. That distribution would resemble a bell curve. There will be a small number of very low skill positions with very low wages. And on the other end there will be a small number of very high skill positions receiving very high wages. And in between you reach the fat of the market with average skill positions reaching average wages. The effect of the minimum wage is to create a clumping on the left side of this curve as the people earning wages for extremely low skill work are now earning exactly the same as the wages for those doing more skilled work. And those abnormally low skill jobs that cannot afford to be paid anymore simply disappear.
For instance gas stations used to regularly be full service - you park, pay, and an attendant would fill you up or take care of any routine maintenance you needed. Those jobs went away, in the US at least. And similarly we're currently in the process of gradually phasing out cashiers, which I imagine our grandchildren will look back on with similar quaintness as we might full service gas stations. The point there being that you're left with a higher and higher skill level as the baseline just to enter the job market. And just because somebody's being paid the new minimum, does not mean they're not substantially more valued than others.