It might be magical to you, it isn't magical to anyone actually working with these things that you can trivially change the last layer and have the outputs represent whatever you want. Get some samples, write a loss function, go to work. Suggesting they can only output words/tokens only displays a complete misunderstanding of how they work under the hood.
I've said it before and I'll repeat. Using terabytes of number lists to achieve a decent NLP isn't all that impressive.
Anyone with brain is impressed by the state of the art LLMs. What's next? The latest GPUs aren't impressive because "shoving a bunch of electrons all around the place to do elementary arithmetic isn't impressive"? The difficulty is getting a bajillion little things to come together in a way that is useful. Pointing out that some complex thing is not impressive because it's "just lots of little simple things" is dumb as hell.
And it's quite limited at that despite the impressive ability to store up language corner cases and put them back out.
"an LLM can output whatever you want" -> this right here is approaching magical thinking. I am really clear headed about it's capabilities and limitations, breathlessly describing it's internals as if it implies it's anything more then a first decent NLP interface is the problem and you seem to be indulging in it.