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But a LLM literally does assign a token from a fixed set of tokens (its vocab) to an input, rinse and repeat, until the stop token.

Classifiers have been giving logits since decades ago.

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Sure, but then there's no such thing as a network that isn't a classifier. Every physically computable function that terminates in finite time will map an input to a fixed set of outputs. And it goes against the common usage, where in machine learning we talk about classifiers, regressors, generative models, etc. as different things. They all become classifiers.

The parent commenter was trying to draw some insight from LLMs being classifiers that wouldn't apply equally to everything else.

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