One day Congress was notified that the threshold had been reached for calling an Amendments Convention to discuss the direct election of senators. This caused panic in the Senate because senators were afraid that a convention would formulate an amendment that would require the election of the entire Senate by the people in one fell swoop rather than phase in the amendment by two-year senatorial "class". Accordingly, the Senate passed the current version of the 17th Amendment, and the House followed quickly.
But shouldn't an Amendments Convention been called anyway? After all, the two-thirds threshold had been reached.
It turns out that some petitions from state legislatures for an Amendments Convention to discuss the direct election of senators had a Discharge Clause. This clause said that if Congress passed an amendment to handle this topic, the state petition would be considered "discharged". Enough petitions contained Discharge Clauses to permit Congress to say that the two-thirds threshold had not been reached. This is how Congress weaseled out of calling an Amendments Convention. But it the states who made the decision to include Discharge Clauses, so it was legally acceptable.
We are talking about two different aspects of that event. It was urged because some US Senate seats (Vermont I think and others) were left empty. These results provided the impetus for an amendment and Congress apparently had no appetite to draft such an amendment (Of course! They never want anything in their world to change.)
Congress did take it out of the hands of states for various reasons some of which you have described but primarily I think because they wanted to short circuit precedent of an Article V event.
Still, it was an amendment that was wholly unnecessary as it was only a few states that had the problem of not seating US Senators. And those states it seems could easily have passed laws or their citizenry could have voted to amend their state constitutions to have interim US Senators appointed by their Governor.
It may have been better for the nation to have had at least one Article V process completed for the history books. I can think of no meaty, no essential reason for staggering the election of US Senators. Any explanation for such I would guess is self-serving, contrived to preserve the status quo or an exercise in sophistry. Let them all swear in at the same time.
BTW your history background is awesome. Thanks for filling in the gaps of the motives and intents of the people of that era.
Indeed human nature does not change.