I don't see it as a threat. I see it as simply a desire to preserve data in the event actions by Trump or his administration are discovered to have been illegal. I would would feel that way regardless of political party. I loved Bill Clinton, but I'm happy that Linda Tripp told Monica Lewinsky to save that darned dress. Maybe because I'm in market research, I believe you can never have too much data.
Now, if people want to delete tweets, that is their prerogative. I'm not against free speech. If by chance I wake up tomorrow with a conversion experience that makes me a conservative Republican, I doubt that I would delete any of my posts on this forum, but if I did, it would be your right to have saved them and use them against me in the future.