I saw a lot of claims on the links but no source documentation to back them up. Please provide primary source documentation that shows there was widespread corruption. I was asking for a source on this part of your statement, "It would just give more power to the greedy state governments."
Here is a book written in 1912 that contains some articles relating to the direct election of Senators. Many of these are transcripts from debates made from the House and Senate floor regarding the issue. Others are newspaper and magazine articles from that time.
Selected articles on the election of ... - Google Books
Page 11 mentions how state legislatures get deadlocked with regards to appointing their Senators.
Page 14 mentions that it will do away with "deadlocks, scandals, and the purchase of senatorships," and that it will "eliminate bi-partisan intrigues."
Page 56 has a speech from William Jennings Bryan that mentions it: "We know that to-day great corporations exist in our states, and that these great corporations, different from what they used to be one hundred years ago, are able to compass the election of their tools and their agents through the instrumentality of legislatures, as they could not if senators were elected directly by the people."
Page 60 mentions how the party system has spoiled the election of Senators by state legislatures. He also mentions how "In the East and Middle West it has become so common for the press of the country to charge that the senators from those states bought their seats that it has ceased to be a matter exciting public comment."
Page 63 mentions how direct election of Senators would make Senators more careful about granting subsidy bills to a particular industry but not subsidies to other industries.
Page 65 the Senator mentions a scandal from his own state and a scandal from Illinois regarding how their state legislatures appointed Senators.
On page 71, it has William Sulzer commenting on the passage of the 17th Amendment.
Debaters Handbook Series: Election of United States Senators said:
We witness to-day in the personnel of the United States Senate the supplanting of representative democracy by representative plutocracy. Here is the last bulwark of the predatory few. Here is the citadel of the unscrupulous monopolies. And more and more the special interests of the country, realizing the importance of the Senate, are combining their forces to control the election of Federal senators through their sinister influence in state legislatures.
Page 100-101 lists among several reasons why the 17th should be adopted
Debaters Handbook Series: Election of United States Senators said:
It will afford a prompt and efficient remedy for the manifest evils made possible by, and unfortunately resulting too frequently from, the present system of senatorial elections, namely, the great length of time consumed in the election and resulting frequently in a failure to choose, the consequent distraction of the legislative mind from important legislative business, and the political and personal controversies, ill feeling, and strife which are the usual - the almost inevitable - accompaniments.
Debaters Handbook Series: Election of United States Senators said:
It will render less possible, and therefore tend to the discouragement of, the use of improper means to influence the control of senatorial elections.
Debaters Handbook Series: Election of United States Senators said:
No reform movement will so effectively as this tend to the destruction of 'boss rule' and the elimination of political 'bosses' from American politics in state, county, and municipal elections.
On page 106, one article states
Debaters Handbook Series: Election of United States Senators said:
As for the nature of the choice exercised by legislators, it is utterly different from anything that the framers of the Constitution had in mind. In their plan for the election of senators, as in that for the election of the President and Vice-President, they failed to take into account the existence of organized parties. Their scheme for the indirect choice of the President and Vice-President became unworkable as soon as the party system was clearly recognized; and, owing to the circumstance that the electors had no other function that that of making this choice, there was no difficulty in nullifying the constitutional scheme. As the members of a legislature have other functions, they, of course, cannot be chosen simply as representatives of a given candidate for the senatorship; but the party system makes it impossible for them to make their choice in any such way as was contemplated by those who made the Constitution.
On page 111, another article states
Debaters Handbook Series: Election of United States Senators said:
The Illinois Legislature that sent Mr. Lorimer to the Senate was deadlocked for many weeks and unable to preform its proper duties as the law-making body of the state because of its subjection to the game played by the desperate and unscrupulous interests that were contending over the choice of a senator. There was no scandal in the election of a Governor for the State of Illinois, and if it had been left to the direct decision of the voters whether they wished to give Senator Hopkins another term or preferred somebody else, a decision would have been reached that could not have been brought into question. Lorimer would never have been a candidate before the people of the State of Illinois, for under no circumstances would they have elected him to the Senate. He has been a powerful, though often unsuccessful, political boss in Chicago, and he and his friends knew how to provide the inducements that finally broke the Hopkins deadlock and elected Lorimer. The confessions of men who had been concerned with the giving and taking of large money bribes, and the subsequent evidence developed in prosecution in the Illinois courts, have made it plain to all readers just how the thing was done.
If the people of Illinois, regardless of party, could to-day express their opinion upon the usefulness of the present method of electing United States senators, their verdict against it would be well-nigh unanimous. They have seen their legislature demoralized and held up to the score and derision of the entire country. They have seen it rendered unfit for its task of legislation by reason of undue strain and excitement over an election that the people themselves could have managed without embarrassment. They now witness the spectacle of the United States Senate diverted from its appropriate duties and engaged in a restudying of the disgusting details of the legislative corruption at Springfield. There is nothing whatever that commends the present system to the people of Illinois, and there is much that condemns it.
There are those who fall back upon the constitutional provision and declare that the plan devised by the founders of the Government is still good enough. But they forget the fact -- or choose to ignore it -- that our present way of electing senators is grotesquely different from that which the Constitution prescribes and intends. The Constitution intends, and means to prescribe, that the entire legislature, including every individual member of it, shall take part in the actual choice of a United States senator. As a matter of fact, under the existing system, a senator is usually not chosen by the legislature in any true sense. He is chosen by the party caucus of the party which has a majority of the members of the two houses of the legislature on join ballot. It is regarded, under the present system, as virtually necessary for legislators elected in the usually way on a party ticket to enter the party caucus and to abide by the result. Thus, if the legislature has 150 members, of who 76 are Democrats and 74 are Republicans, it is the almost invariable opinion of strict party men that the majority choice of the Democratic caucus ought to be promptly accepted by the entire legislature. Under this system, every one of the 74 Republican votes must be thrown away. They will be expended upon a complimentary vote for some Republican who cannot by any chance be elected. If the Democratic caucus should be closely divided between two candidates -- the one representing, as is so frequently the case, the private choice of the machine or the boss, and the other representing a decent public opinion and some regard for the traditions of statesmanship -- it is nevertheless the doctrine of the party man that if the machine candidate can be forced through the caucus by a majority of a single vote, every man who has gone into the caucus must accept the result and the man must be elected in the face of an outraged public opinion. Thus 39 men would control a legislature of 150 men.
More about William Lorimer and how allegations of bribery in the Illinois state legislature to attain the senatorship of Illinois can be found here. It is a copy of the findings of the committee tasked to investigate this corruption.
Proceedings before the Committee on ... - Google Books
The following is a link to a magazine article published in 1900 that exposes William A. Clark, a businessman who made a fortune in gold and moved to Montana to become a political boss, bribed several state legislators $10,000 for their vote in electing him Senator.
The literary digest - Google Books
The following is a link to a book of Senate election cases, and mentions how W.G. Conrad, William A. Clark's opponent for the Senate seat, paid between $5,000-$10,000 in bribes to committees of state legislators to get the Senate seat. It was written in 1913.
Compilation of Senate election cases ... - Google Books