Dr. Steven Dykstra, an adolescent psychologist and a founding member of the Wisconsin Reading Coalition, explains why nonsense words are essential for assessing phonics decoding skills.
The biggest argument for nonsense words in assessment (not always in screening, but certainly in diagnostic assessment when indicated) is that it lets us isolate a given skill from other skills which could be used to compensate. When I show you a nonsense word I know you don't have it in your memory because you've never seen it before. You can't rely on anything except phonological decoding skills so I know I'm assessing your phonological decoding skills and nothing else. You can't recognize the word from memory because you've never seen it before and you can't infer it from context because there is no context.
If I want to assess the strength in your right arm I could ask you to lift weights. But I have to make sure you don't use your left arm, or your legs, or your back, or the muscles around your shoulder to lift the weight. If I want to assess the strength of your bicep I have to make sure you can't use other muscles to make up for your weak bicep
Arguing that reading nonsense words doesn't directly mimic to authentic reading is beside the point. If you ever have a careful neurological exam of your cervical spine the doctor will ask you to flex and move your fingers in very specific ways. None of these movements are ever performed in isolation in day-to-day living, and none of them can't be supplemented with other movements to compensate in case there is a problem. But isolating them lets the doctor determine the specific nerves that might be damaged and the exact spot in the spine that might be involved. That's why they do it, not because it mimics actual movements people do in their lives, but because it provides essential information.
I suppose if some doctors practiced "Whole Neurology" or "Balanced Neurology" they would object to those exams, but they'd be wrong and their patients would suffer for it. Of course, that would never happen because the profession wouldn't allow it and malpractice lawsuits would punish it.