You may be correct from a Constitutionalist point of view.
However who knows with Schumer running the Senate?
Pelosi didn’t even run the first impeachment through the Judiciary Committee (Nadler), instead she used House (un)Intelligence Committee (Schiff) as her “point man.”
These Democrats don’t give a shit about the Constitution or historical precedent.
Constitutional monkeyshine like Wickard v Filburn is one thing, but if they’re going to shine on the Constitution at this level, that’s prima facie evidence of an actionable violation of the Oath of Office. At least, it is under the Rule of Law.