Seems trivially demonstrable because you can just chain things forever?
Mary ran after the dog and the dog was brown and a cat came along and…
Mary ran after the dog and the dog was brown and a cat came along and…
I think you're going to find out that no, you can't, and this impossibility is going to trivially demonstrate itself.
Both viewpoints are useful, they can prove general properties that hold for arbitrary long sequence of words and you put a practical bound on that length.
That's clearly false. It's not about some platonic mathematical simplification. Humans patently do not fit the Chomsky criterium for intelligence.
In fact, I'm pretty sure it's physically impossible for any real being to fit it.
Well, yes and no. Constructing this "infinite" sentence will run into some serious problems once the last star burns out, possibly sooner.