The courts are the final arbiter of constitutionality, not the Senate.
The Supreme Court has unanimously decided that
all questions regarding the political impeachment, trial, and judgment for misconduct of government officials belong solely and exclusively to the Congress and that the Court is not allowed to review those decisions. The Court has declared that to intervene in any way would be a violation of fundamental separation of powers embodied in the Constitution and a violation of the clear language and intent of the Constitution for a multitude of well established constitutional principles and precedents. One of those is that as neither the executive or legislative branches are given constitutional authority to over rule decisions made by the Court, the sole check on the power of justices of the Supreme Court, once nominated and confirmed, is impeachment by Congress. Impeachment is also a check on the power of the Executive Branch.
Each branch of government has power that is granted
solely to that branch by the Constitution and which
cannot be impinged upon by either of the other two branches because that power serves as a check on the other branches competing for power. For Congress, impeachment—which is a power given
solely to the House and trial and judgement of impeachment which is a power given
solely to the Senate—is one of those powers that cannot be breached by any other branch.
Even when the Chief Justice presides over a presidential impeachment, it is the Senate that has
final say on any rulings of any kind. Any presiding officer of any impeachment trial in the Senate is bound by senate rules and the vote of the senate. Any ruling by the presiding officer can be challenged by any individual senator which is then decided by a vote of the Senate. Any decisions made by the Senate are final and not subject to review by
any court.
There is no debate about it. It is settled Constitutional law.