Shouldn't the President's Twitter library be at the end of his term?

We’ve noticed that there is a concerted effort by many people within the administration ― and from without ― who wish to silence the President’s tweets. Say what you want about Donald Trump, he may not be good at president-ing or leading or geo-politics, but he is a damn fine Twitterer. Probably the best that ever lived.
And so we thought at “The Daily Show” we would take a moment to honor the President of the United States and the King of Twitter with this library.
Now some people would say, “Trevor, why would you have this Twitter library now? Shouldn’t a presidential library be at the end of a president’s term?” Yes, that is true. Unfortunately, we do not know when the term will end. Could be next week, could be never. So we decided to do it now. Tell the ones you love you love them when they’re still around.
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Trevor Noah And 'The Daily Show' Just Took Donald Trump Mockery To The Next Level

One reporter noted that "No reporter wants to silence Trump's Tweets" even when they legally are harming him daily in his fight against obstruction of justice charges.

It's sort of like (in a court of law) shooting yourself in the foot with each tweet. The end result likely will be: "Trump impeached".

I think everyone who tweets might take a lesson (regarding a court of law) and their lives as to how Trump likely is ending his presidency through his tweets. Because Tweets CAN be used in a court of law against you,  against even Trump.