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.
In 1829, Andrew Jackson asked in his State of the Union letter that Congress pass two constitutional amendments: one for the direct election of senators; the other for the direct election of the President, thus abolishing the Electoral College. Jackson had run on the slogan "Jackson and Reform", with his target being the use of wealth gained from industrialization for the corruption of the political process.
At the time of the Founding, wealth came from the land, which is why only property owners could vote. Two Framers had a clear vision of what America would become if industrialization broke out of the Northeast: Hamilton and Jefferson. Hamilton saw a glorious industrial and commercial nation, and he embraced the future. Jefferson had a Celtic sense of the love of the land and wanted a nation of farmers. He feared a nation of industrialists, cities and an un-propertied proletariat grubbing for the levers of power. Ironically, the one issue where the two men agreed was the concept of stakeholder franchise, i.e. only property owners should be allowed to vote.
With industrialization, wealth no longer came from the land, but from manufactures. This was the kind of wealth that only a few of the Framers could have envisioned. Rather rapidly, wealthy industrialists bought local and country governments, and moved on to buying state governments.
In factory towns, the owners would line up the employees in rank and file, and march them to the polling place. The County Clerk, usually an officer of the company, would take down their votes because the Progressives had not yet imposed the secret ballot on the nation. If a man voted the wrong way, he would lose his job, his company housing, his company scrip -- and in jurisdictions where it was impossible to tell where the sheriff ended and the company goon squad began, he could lose his life.
Jackson had favored strict regulation of corporations, and there was quite a bit of regulation at the state level. Some states only granted corporations a ten year life before requiring reorganization. But the influence of money was permeating every level of government. Because state legislatures elected senators, this corruption leached into the federal government via the Senate. As a result, over time the senators from Pennsylvania became known as the "senators from King Coal". Senators from Montana were known as the "senators from Anaconda Copper". The senators from California were known as the "senators from the Southern Pacific Railroad". This became more pronounced after the Civil War because Lincoln was working from Hamilton's template. If you go to my essay on federalism, you'll see what the Progressives were pushing for: the secret ballot, open primaries, giving the vote to women, and the direct election of senators.
What is interesting is that all the 17th Amendment really accomplished was to move the locus of corruption from the state legislatures to Washington. In effect, the 17th Amendment created K St.