Heather Cox Richardson, author of West from Appomattox, The Death of Reconstruction, and The Greatest Nation of the Earth, as well as all-around brilliant historian and fine human being, writes apropos this discussion and this one:

By the way, Hannibal Hamlin was on the ticket in 1860 because he was from Maine, and Maine voted before any other state (hence the saying, “As Maine goes, so goes the nation.”) Lincoln needed the momentum he could get from having a local boy on the ticket in 1860. HH was jettisoned in 1864 to broaden the party into a national concern. Johnson, a border state man who had stayed with the Union, seemed the logical choice.

“Logical” does not in this context mean “good.”