I see a fair amount of bullshit in the LLM space though, where even cursory consideration would connect the methods back to well-known principles in ML (and even statistics!) to measure model quality and progress. There's a lot of 'woo, it's new! we don't know how to measure it exactly but we think it's groundbreaking!' which is simply wrong.
From where I sit, the generative models provide more flexibility but tend to underperform on any particular task relative to a targeted machine learning effort, once you actually do the work on comparative evaluation.
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.