Because if the minimum wage is too high, employers can't afford to pay it, so it will just result in reduced employment rather than wages going up, aka economic "deadweight loss".
That much is obvious. What is in question is the effects of more realistic minimum wages like this one. Some claim that _any_ minimum wage will only result in deadweight loss, which is true in simplified models, but the effect in the real world is not so clear, hence the need for this type of research.
Yes, I agree: this research shows that governments do a poor job when they attempt to set minimum wages, and they would do better to focus on accomplishing income redistribution policies through the tax code.
When government tries to set minimum wages, they often result in job losses (or foregone jobs that were never created) which, as you wrote, is known in economic circles as "deadweight loss."
That much is obvious. What is in question is the effects of more realistic minimum wages like this one. Some claim that _any_ minimum wage will only result in deadweight loss, which is true in simplified models, but the effect in the real world is not so clear, hence the need for this type of research.