GenAI models are meant to create, not retrieve. The model being able to sometimes reproduce copyrighted material in training data is an unintended side effect, and usually requires the user to intentionally cause it to happen. Their business model is indeed a "magic painter" (and/or "magic writer", "magic coder", etc.), which is IMHO valuable and fair - again, it's meant to create, not reproduce or retrieve.
I indeed confused LLM/foundation models and GenAIs. They are both the current tech trend and both fall under the category of AI productivity tools, and I agree with your point.
