But when that colony section allows it's economy to become totally dependent on that single sector, to the almost total disregard of other sectors of the economy then they are taking basic capitalism and making it work against them.
What other sectors would those be? Industrial plants? They had them where they needed them at home and, acting consistently with capitalism, traded their comparatively advantaged agricultural goods for the remainder abroad. From a capital standpoint, such an action is common sense - you produce what you are best at and will make you the most money, and what you aren't good at producing you purchase from somewhere else that is good at producing it.
I suspect that you have a job, correct? If so, you should know this. It's the same reason why you don't spend your days knitting shirts - your time is better spent at something else, namely whatever your job may be, even though you probably need shirts as well. So instead of knitting them on your own, even though you theoretically could do that, you instead go to Wal-Mart and buy them there with the money you earned at the job where you do spend your time.
then they are taking basic capitalism and making it work against them.
Nonsense. As is evidenced by the statistics of the time, the southern states were among the wealthiest in the nation. Rather than waste their time knitting shirts when they could be making money at something they were better at such as agriculture, they made their money at agriculture and went to the 19th century equivalent of Wal-Mart for the shirts. The end result? The south gets rich. I don't know about you, but to me that sounds as if capitalism was working quite nicely for them.