Some of this goes back to the constitution:
AMENDMENT VI
In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial, by an impartial jury of the State and district wherein the crime shall have been committed, which district shall have been previously ascertained by law, and to be informed of the nature and cause of the accusation; to be confronted with the witnesses against him; to have compulsory process for obtaining witnesses in his favor, and to have the Assistance of Counsel for his defence.
The prosecution needs to be up front about what they are alleging, and if they were to go second, they could pull some gotcha shit and be like "Derek Chauvin had a 500-page manifesto in his house declaring his intention to kill a Negro male" and the defense would be like "Aw shit." And if the defense went first, they could present all kinds of information about how this manifesto was really a screenplay and the prosecution could be like "Welp, we weren't going to mention it, but since you brought it up...."