I think Perryville is the best answer to Old Reliable's question; but my discussion of what the Confederate Army could have done is as stupid as Bragg's choices were. There was no profit in the rebel armies turning west, as they did; and West Point is the last place they should have headed for. Avoiding Buell and reaching the Ohio was the correct strategy; but, having already taken control of Lexington and Frankfort and assured the installation of Richard Hawes as governor, why would Smith and Bragg not continue north to Covington? They had the logistical advantage of the Kentucky Central railroad which could supply them with the food and horses from Kentucky's best farmland. They would have forced Buell to chase them up the Ohio from Louisville without his gunboats along terrain that is as difficult as marching along the Hudson north of Peekskill is (the similarity is my only excuse for thinking of the two West Points).Perryville
Lincoln had won the Presidential nomination by being the candidate who could win over the Know-Nothings in the Midwest. Fremont had lost to Buchanan because he could not appeal to enough of the voters in Illinois, Indiana and Pennsylvania. If Bragg had made his objective reaching the Ohio River instead of whipping the Yankees, that would have changed the entire political balance in the Midwest. It is 72 miles by road from Perryville to West Point, which gets its name from being the same kind of chokehold loop on the waterway that West Point is on the Hudson. The Democrats picked up 27 seats in the 1862 election and reduced the Republicans' control of the House of Representatives to a plurality; the shock of the news of the Rebel Army's cannon attacking traffic down the Ohio would have been decisive.
The news of a Confederate Army standing across the river from Cincinnati in 1862 could have Ft. Sumter in reverse as far as Kentucky and the lower Ohio were concerned. Anyone reading the newspaper in the Ohio Valley would have had to think: do we really want to go to war with these rebels or just sell them hogs and corn as we have been doing?