The reason there was no advantage to doing so was because of the navigation act of 1817. Charleston was as you said, much smaller, and could not handle traffic like New York, but this is self reinforcing condition. If it can't get the traffic, it can't grow, and if it can't grow, it can't increase it's capacity. The navigation act made the costs of going to Charleston the same as going to New York, and it was not only 800 miles further away, it didn't have the facilities to handle great quantities of shipping anyways.
Getting rid of the large tariffs, and getting rid of the ban on carrying cargo between ports, and it is instantly profitable to sail to Charleston, sell part of a cargo, then sail to Pensacola, and sell another part of the cargo, and then sail to Mobile, and sell the rest.
Instant money for Southern ports. Greater profits for European traders.
The money streams would have deflected from New York, and gone to the same places where the American export cargoes originated. The New York middlemen would have been cut out.
"...the mask has been thrown off and it is apparent that the people of the principal seceding states are now for commercial independence. They dream that the centres of traffic can be changed from Northern to Southern ports....by a revenue system verging on free trade...."Boston Transcript, March 18, 1861.
A year or so ago I read an article from some Charleston newspaper shortly after South Carolina seceded. It was full of stories about the massive building boom going on at the time, and how all the warehouse space and hotels in Charleston had been overwhelmed with customers. The city was going like gangbusters trying to build new warehouses, hotels, and other industries.
Charleston would have grown quite a lot, and it would have all come at the expense of the very wealthy people in New York who backed Lincoln's election to the Presidency.
“Getting rid of the large tariffs, and getting rid of the ban on carrying cargo between ports, and it is instantly profitable to sail to Charleston, sell part of a cargo, then sail to Pensacola, and sell another part of the cargo, and then sail to Mobile, and sell the rest.”
well and good, except it would have been British flagged ships that were running the coastal trade, not Southern ships.
“Nobody bothered to build trade between Charleston and Europe because there was no advantage to doing so.” How much Southern cotton was shipped out of New York or Boston. Bet Charleston shipped a whole lot more cotton than New York did. A southern owned ship could easily carry a load of cotton bales from Charleston to England and return with a load of English goods to Charleston. There was no law to prevent it.