Trump should just nominate himself so he can be in power forever.

He could and, moreover, contrary to other answers, it’s not actually clear if he’d be required to resign as President to take the position. Let’s look at the Ineligibility Clause of the Constitution:

No Senator or Representative shall, during the Time for which he was elected, be appointed to any civil Office under the Authority of the United States, which shall have been created, or the Emoluments whereof shall have been [increased] during such time; and no Person holding any Office under the United States, shall be a Member of either House during his Continuance in Office.

It only applies to Members of Congress, which is why it’s under Article I (Section 6, Clause 2). It does not (explicitly) apply to any relationship between the Executive and Judicial branches of government.