Such as with the $15 minimum wage - it's the marginal businesses that will shut down, and the people with marginal job skills who will be shut out of the job market.
Thinks are complicated. All the dot-to-dot statements are somewhat true, but they're all going on at the same time. Higher minimum wage means more spendable cash, which means more small businesses see an uptick in sales, so more profit. See! I can do it too.
Deadweight losses are the inevitable leftovers of decreased efficiency after they have been drawn.
(Yes, I know that often businesses miscalculate the value of an employee, and it may have other sources of profit that cover the losses, etc., but it doesn't change the reality that the profit motive will squeeze such things out.)