Yeah, Wordle itself is not that complicated, and as you said, other than serving the HTML and JS it requires no server-side processing. I'm definitely going to download the HTML and JS and rehost it, at least just for myself privately.
To me, that's further reason why the Wordle purchase is sad. NYT is essentially buying some HTML, CSS, JS… and a playerbase. Rather than competing by improving their existing puzzles and/or creating new ones, they're just buying out the competition.
Even though technically-minded people like you and me will be able to re-host Wordle quite easily, the general public who lack those skills will still eventually lose access to the original independent Wordle.