For what it is worth, that very phrase, the Senate as a "millionaires club", originated in the 1890s, well before the direct election of senators.
Indeed, at the Senate's own website, you have this recounting of the Senate under Vice President Morton (1889-1893):
The Businessman's Cabinet and the Millionaires' Club Just as Harrison's cabinet was called the "businessman's cabinet" for its inclusion of Wanamaker and the Vermont marble baron Redfield Proctor, the Senate over which Vice President Morton presided was dubbed a "millionaires' club." In the late nineteenth century, businessmen had steadily gained control over both the Republican and Democratic parties and used their political positions to advance their economic interests. Senators became identified as spokesmen for railroads, timber, mining, and other industries. As California Senator George Hearst, who had made his millions in mining, proclaimed: "the members of the Senate are the survivors of the fittest." It seemed appropriate, therefore, that the Senate's presiding officer should be one of the nation's most prominent bankers.
(Trivia note: not only was Vice President Morton one of the nation's most prominent bankers, but the infamous community of Morton Grove was named in honor of Vice President Morton, albeit that naming was many years before he served as vice president.)
I believe it is self-serving politicians, such as we seem to be infested with, and lack of real statesmen that is bringing down the nation.