is Asyndeton just bad grammar?

No, asyndeton is not bad grammar. It is a rhetorical device that is used to omit conjunctions between words or clauses in a sentence. This can be done to create a sense of urgency, emphasis, or surprise.

Bringing it To Your Story

I just came from a conversation which brought up a peeve of mine. This Be a good reader, to be a good writer. I want to assure you, that if you don't know what you are looking for, you're not going to suddenly recognize it from reading. Not from any author worthy of study. Because right now, you don't know enough to ask the question -- which isn't a slight. Not at all. Here are couple of examples of techniques being used which are going to slip under the radar. But maybe they will spark enough in your writer's mind to figure out a few others.