Why is this even a question? Of course his tweets should be preserved. He's the one who has chosen not to have his tweets vetted or reviewed. He's the one who has chosen to show the entire world the stuff that flitters through his brain. This is who he is. And as such, for better or worse it is a part of American history. It is on public record and must be considered like any other written or recorded medium a POTUS uses to communicate. POTUS is a 24/7 job - there are no time outs. If you're POTUS and you're writing something that is available to the public, guess what? It's part of your legacy.