I think we have a vocabulary problem here, because I am having a hard time understanding what you are trying to say.

You appear to be comparing apples to oranges. A generation task is not a categorization task. Machine learning solves categorization problems. Generative AI uses model trained by machine learning methods, but in a very different architecture to solve generative problems. Completely different and incomparable application domain.

I think you're overstating the distinction between ML and generation - plenty of ML methods involve generative models. Even basic linear regression with a squared loss can also be framed as a generative model derived by assuming Gaussian noise. Probabilistic PCA, HMMs, GMMs etc... generation has been a core part of ML for over 20 years.

And yet, people very often find themselves using generative models for categorization and information retrieval tasks...