I think you're under the impression that the difference between those things is far greater than it actually is. Large Language Models work by developing statistical maps of associations. That's discrimination. They're a direct evolution of categorization models. The ability to associate a hash of a JPEG with "cat" is the same as the ability to associate "How are you?" with "Great, how about you?" It's all associative mapping. LLMs are just the current leading edge of that technology. If you want to, for example, generate a list of tags that describe a document, an LLM is the best tool we currently have for doing that.

To put it another way, what you term "discriminative AI" is "generative AI." It's generating a category or list of categories in response to an input. That's not functionally different than generating a sentence in response to a sentence, it's just an order of magnitude less complex. You can argue terminology but the technology exists on an evolutionary curve, with no real hard boundaries.