First of all, none of the occasions (now three) when an impeachment has been considered by the Senate after the person impeached was no longer in office led to a vote of conviction. In each case, at least some Senators voted against conviction on the ground that the proceedings were not constitutionally authorized. If Trump, or any other official, had been convicted and disqualified after leaving office, that would have established a clearer precedent.
Secondly, because the Senate establishes its own rules of procedure, and no Senate can bind future Senates, which are free to adopt different procedures, and to handle impeachment in different ways.
Thirdly, because of Nixon v. United States, 506 U.S. 224 (1993). In that case Federal judge Nixon (a different person from President Nixon) had been convicted of and imprisoned for perjury, but refused to resign. Nixon was impeached by the House. A Senate committee looked into the matter, and delivered a report to the whole Senate. The Senate then voted to convict Nixon and remove him from office without holding any more formal proceedings or hearing witnesses. Nixon sued, claiming that this was not a "trial by the Senate" and did not meet the constitutional standard for dealing with an impeachment. As the Wikipedia article puts it:
The majority opinion, by Chief Justice William Rehnquist, held that the courts may not review the impeachment and trial of a federal officer because the Constitution reserves that function to a coordinate political branch. ... Justices Byron White, Harry Blackmun, and David Souter concurred, but voiced concern that the Court was foreclosing the area for review. While they found that the Senate had done all that was constitutionally required, they were concerned that the Court should have the power to review cases in which the Senate removed an impeached officer summarily without a hearing, or through some arbitrary process such as "a coin toss."
If the House were to purport to impeach, and the Senate to convict, a person who had never held federal office, Nixon v. United States would, on its face, prevent the courts from interfering. But in such a case of obvious overreach, I suspect that case might be distinguished and the courts might act. No such case has ever arisen, nor seems likely.
But an arguable case of procedure in an impeachment matter cannot be reviewed by the courts without overturning Nixon v. United States, so no court decision can establish the propriety of a Senate trial after the accused is no longer in office.
Note that the opinion by Justice White in the Nixon case (which agreed with the outcome, but not the reasoning of the majority view) incoluded the statement that:
In essence, the majority suggests that the Framers' conferred upon Congress a potential tool of legislative dominance yet at the same time rendered Congress' exercise of that power one of the very few areas of legislative authority immune from any judicial review. ... it is the Court's finding of nonjusticiability that truly upsets the Framers' careful design. In a truly balanced system, impeachments tried by the Senate would serve as a means of controlling the largely unaccountable Judiciary, even as judicial review would ensure that the Senate adhered to a minimal set of procedural standards in conducting impeachment trials.
This seems to confirm that the Nixon case denied any role to the courts in determining the propriety of impeachment proceedings. While that decision stands, the Court is unlikely to rule on what is or is not done in the course of Senate prodeedigns on an impeachment.
