Some damn fine men have emerged from brokered conventions. Garfield, Harding, Coolidge...an argument could be made that Jefferson could be included in that list.
First, Harding and Fine Man is a seldom used combination of words. Monumentally corrupt embarrassment to the Republican Party might be more accurate. Garfield was a fine man and emerged as a compromise candidate (that was also true of Harding in 1920) out of the 1880 convention but served only 200 days till he was assassinated and died. So it's hard to describe him as a great president. We'll never know. And Coolidge was Harding's VP who took over after Horn Dog in the closet with his mistress in flagrante delicto / Teapot Dome Scandal Warren died of natural causes in office.
Finally, in Jefferson's time there were no formal (informally there were the Democratic Republicans - today's Democrats - and Federalists - now defunct) parties nor any conventions to nominate a presidential candidate. He was Adams' VP and replaced him in the election of 1800. His Vice President, Aaron Burr, got that office by virtue of coming in second in the Electoral College vote.
The last really contested convention, and even this one was still a single ballot affair, was probably the Democratic convention in 1960 with Kennedy barely winning and adding second place Johnson to the ticket for party unity.