Since the Civil War, American government has slowly moved away from such "indirect" elections of leaders and moved closer to full, direct democracy. In my opinion, such a system of government is incompatible with a constitutional republic such as the one our founding fathers created. Successful "leaders" have come to be defined as the ones who do the best job of pandering to the tastes of an electorate that is increasingly ignorant and vulgar.
Without the 17th Amendment, people like Al Gore, Joe Lieberman, and Trent Lott would never have been elected to the U.S. Senate.
The original wording of Article I, §3 was "chosen by the legislature thereof". Popular election of Senators didn't start until the late 1800's when numerous state legislatures were having trouble electing the Senators. By the time the 17th was proposed, I think perhaps 15-20 states already had popular elections.