Did it? A lot of it ended up here ...
... or in mansions like it. Or in the furnishings and gardens. Or in agricultural equipment, seed, livestock and land. Or in slaves.
Some was in banks in New Orleans or Charleston or New York or London. Some went to pay for shipping and insurance.
If you lived in a very agrarian part of the country, you'd be buying stuff that was made elsewhere, so it made sense to keep some of your money with commission merchants or cotton factors who sold what your plantations produced and bought the things you wanted or needed. Much of the money you made in the harvest would have to be spent on planting the next crop, so it didn't make sense to take it in cash and spend it all or stuff it in your mattress.
Western banks tended to be newer and less experienced and more likely to collapse when panics (what we'd call recessions or depressions) broke out. Western state governments also overextended themselves and became insolvent, leaving their bonds worthless. Those were two more big reasons why plantation owners in the Old Southwest may have liked to spread out their investments and keep some of their money in Northeastern or foreign hands.