Some people may not be allowed to delete (or to be deleted by someone else) their "tweets". US Presidents are one such category of people - all of their works while in office belong to the country.
https://en.wikipedia.org/wiki/Presidential_Records_Act
In some lawsuits, records such as tweets need to be produced in what is called "discovery". It is possible to lose lawsuits - by default - for either destroying or refusing to turn over such records. A modern example of how expensive such behavior can be would be to look at how much Alex Jones is going to be paying out.