Even when the country has been in a "reforming mood" those reforms have usually been limited. Direct election of senators is really only a minor change. Reclaibrating the political landscape as this thread proposes would be rather more revolutionary.
If you mean my "third senator" suggestion, or the moving of Senate elections to odd numbered years, you are probably right. Afaik not even Bryan or Champ Clark ever advocated them.
However, if you mean the six-year-term Amendment itself, this seems to have had plenty of support. In particular, it received 13 Senate votes from the Old Confederacy, to only one opposed. The lone dissenter was a Tennessee Republican who had been appointed by the Governor to fill a vacancy, and would never have been chosen by the Legislature. The Old South was not much given to returning dangerous radicals, and its Senators seem to have been happy enough with the idea.
Also, of course, this measure was passed by a lame-duck
Republican Senate - 51R-44D. Since the Dems picked up seven more seats in 1912, this indicates that the composition of the Legislatures was still moving in their favour - good news for the Amendment.
One final point. As I noted earlier, out of thirteen Constitutional Amendments sent to the States in the 20C, only two - the Child Labor Amendment and the Equal Rights Amendment - were rejected. Further googling confirms what I had already suspected, that in each case the defeat was due to strong opposition from a particular section. Of the twenty states not ratifying the CLA, thirteen were Southern or Border States, and ditto for ten of the thirteen which never ratified the ERA. By contrast, there seems to have been no such sectional opposition to the 6YT Amendment. By my count the breakdown in the Senate was as follows
South - 13Y, 1N, 8NV [1]
Border [2] - 5Y, 3N, 4NV
Northeast - 8Y, 6N, 4NV
Midwest - 8Y, 9N, 4NV [3]
Mountain - 10Y, 2N, 4NV
Pacific - 3Y, 2N, 1NV.
Only in the Midwest did a plurality of Senators reject the Amendment, and there only by a single vote. It seems to have enjoyed substantial support in every region, and massive support in two (South and Mountain). Agreed, this does not guarantee ratification, but it suggests to me that if passed by the House (a foregone conclusion had it ever come to a vote there) it stood an excellent chance in the Legislatures, where in most cases only simple majorities were required.
[1] The NYT doesn't give the reasons for Senators not voting, but quite a few of them were probably paired.
[2] DE, MD, WV, KY, MO, OK.
[3] One of the Illinois Senate seats was vacant.