[thaumasiotes]

> Incidentally, Gödel's theorem eventually comes down to a halting-like argument as well (well, a diagonal argument).

> There is a presentation of it that is in like less than one page in terms of the halting problem

Those are two very different ideas. Your second sentence says that Gödel's theorem is easy to prove if you have results about the halting problem. Your first one says that in order to prove Gödel's theorem, you need to establish results about the halting problem.

[ajkjk]

I'm saying that if you want to understand why Gödel's theorem is true, look at the one-paragraph proof based on the halting problem, not the like 20-page one with Gödel numbers.