But at the turn of the century the Progressives made it a priority, and the people strongly agreed. The House agreed, but the Senate balked
If the Senate balked the Senators would have done so at the will of the State legislatures (elected by the people, bearing in mind that "the people strongly agreed") or if they balked in defiance of that will they would have done so at the risk of being replaced with Senators who would not balk.
If the will of the State legislatures was in defiance of those who elected them, that defiance was at the risk of being replaced with others (elected by the people, bearing in mind that "the people strongly agreed") who would not so defy.
The states began exercising their right under Article V to request a convention to address the issue of the popular election of senators.
For some reason, the states (whatever you meant, I mean the state legislatures here, but that will change) " began exercising their right under Article V rather than replacing the defiant Senators.
For some reason, the states (whatever you meant, here I mean the people who elected the state legislatures, changing as I said I would) " began exercising their right under Article V rather than replacing the defiant State legislators who would in turn replace the defiant Senators.
It is not obvious why the states (given any meaning) would began exercising their right under Article V when they had agreement and authority to attain their ends through appointment (by the legislature) or election (of new legislators) and subsequent appointment of less defiant Senators. The only reason I can think of would have to do with the time it took to get the job done.
Re a balanced budget amendment:
but then the issue fizzled.
In other words, those pushing for the amendment had neither the political wherewithal to attain their objective through the Congressional Method, nor the Convention Method.
Had it not fizzled, we would have witnessed the states taking control from Congress and addressing the issue directly via a convention
But once the tally was one or two states away from a convention call, the Congress could have yielded and passed the amendment, similarly to the way the 17th was passed. That Congress didn't indicates those pushing for the amendment had neither the political wherewithal to attain their objective through the Congressional Method, nor the Convention Method.
Re a human life amendment:
today you would have no chance of getting one through Congress. But the states through a convention?
If the states had the political wherewithal to get such an amendment through a convention, why would they not be able to get it through Congress, electing new Congress members as necessary? If the faction supporting such an amendment is unable to get the kind of Congress critters it needs, what is the reason for thinking it could get the kind of conventioneers it needs?