I don’t know what the Framers were thinking of when they wrote the office into the Constitution. Perhaps they assumed the VPOTUS would function as the POTUS’ prime minister and second-in-command in the executive branch, but it’s never worked out that way. We need a designated successor in case of a president’s death, incapacity or resignation. We do not need a constitutional officer whose only constitutional functions are to be a national spare tire and cast the tie-breaking vote in the Senate. How often are they called on to do the latter anyway? And if there’s no tiebreaker, so what? Let the resolution fail.
I suggest the office be abolished, the VPOTUS’ place in the line of succession to be given to the Secretary of State – the senior post in the Cabinet and arguably the most important. If a president dies in office, it’s better for the successor to be someone who has recent experience in actual, important decisionmaking.