Slaves could have been used for other purposes than picking cotton, like mining and other things. If the South had stayed in the Union, slavery might have lasted till the mide early 20th Century.
But they weren't. If you go to the Wikipedia entry for "New Mexico Territory", it points out that when "New Mexico Territory" extended all the way from Texas to California, there were less than a dozen slaves in the entire region over it's entire history up to the 1860s.
And this was a time when it was legal to have slavery in those regions. There just weren't any, and that's because there was no profit to it.
A slave was much more profitable working a plantation in the growing regions of the South.
So real world evidence shows that your theory that they would have been used, (and how many slaves do you need in a mine compared to a plantation?) is demonstrably incorrect.
If they could have made money with them, they would have used them. Since they didn't, it's evident that there was no profit in it.