The nub of the unorthodoxy can be found in that phrase "as now practiced." In other words, I am saying that a change from using the filibuster rule from how it has been used traditionally --only in somewhat extraordinary circumstances-- and how it has been used by today's Republican Party --as an across the board hurdle for passage of any legislation-- alters the status of the rule and its relationship to the Constitution's expectations regarding the Senate.
The Constitution gives each house of Congress the right to establish its own rules. But does the Constitution allow those rules to supercede the Constitution?
Thus I argue:
The filibuster has become unconstitutional. The filibuster is not even a law. It is just a rule of the Senate. It is below a law, and the Constitution is a level above the law: the ultimate authority.
The Constitution would have measures pass the Senate if they enjoy a majority support. But when the Republicans started using the cloture rule intended for special situations and emergencies--into an across-the-board, "Nothing can pass without 60 votes," it crossed the line of constitutional acceptability.