Somebody asked:Why is the Senate, and not the Supreme Court, deciding whether the current impeachment is constitutional? As an Australian lawyer, I was thinking the same way. If a valid impeachment is on foot, only the Senate can resolve it. But the question here is whether the Constitution allows the impeachment AT ALL, once the person is out of office. If that question is one for the Chamber, every impeachment can be thrown out by the majority party?
It is absolutely true that every impeachment can be throw out by the majority party. This is not so unusual, in Australia, as long as the government represents the majority party, the majority party can throw out every vote of no-confidence.
In fact, except in the historically rare case of a 2/3 senate supermajority, every impeachment can be throw out by the minority party.
The constitution makes it hard to impeach a President. The process requires a bipartisan agreement that the President should be impeached. This is because the President has a source of Legitimacy independent from Congress (the Electoral College, and ultimately Election by the people). While the President carries the support of even a minority in the Senate he/she may continue in the role.
It seems that the Constitutional question can be decided by the Supreme Court, but only if there is a case before them. If the Senate convicts Trump and disqualifies him. Then if Trump files, and a state refuses to let him run, citing the Senate disqualification. And if Trump sues the state arguing the disqualification was unconstitutional, such a case could end up in the Supreme Court. But courts can't decide hypothetical cases. There has to be a litigant who has been harmed.