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Slavery was extremely economical. That was the entire point.
Slaves dug numerous canals in the south. The reasons the south's infrastructure could not compete with the north's were two-fold. Geography and, in a word, "technology".

The canal era in the US was really initiated with the completion of the Erie in NY. All of a sudden, Georgians watched NYC become America's premier port city because of the Erie canal, and concluded that Georgia must build canals if it was to compete. The geography in the South, however, was all wrong. (At least, by the standards of 19th century engineering. And even by today's standards really.) The S-O-A Canal is a very good example. It was started... and less than a year later, southern engineers had to concede that every route from the Piedmont to the Tennessee border was impractical for canal construction. Even in the face of geographic realities like this, slaves were still able to carve out numerous canals in the south. Canals that would have been highly unlikely to have been carved out by any rational means. In the north they would have done the survey, determined the geographic problems and moved on to another project. Slaves proved resourceful and determined problem solvers on many of the canal projects. (The slaves promptly began using many of these canals as escape routes North as soon as they were completed... but that's another story.)

The other reason canals were bad business in the South AND the North was technological. The reality is... railroads simply had a manifest superiority to canals as infrastructure assets.

Between 1825 which is, I believe, when the Erie was completed to about the 1850's, which is when everyone seemingly conceded the superiority of the railroad - the South wasted a lot of time on canal construction. In fact, it could be argued that what held the South back was its insistence on building canals after witnessing the success the North was having with them. It took them a lot of time before the South fully considered the gift of geography the North had been given in their analyses. (The upper midwest sits on something like 20% of the GLOBAL freshwater supply. And that's just for starters. Look at a topographical map of NY State and trace out the Erie Canal on it and you'll see what I mean.) The correct strategic response to Northern canals would have been to invest heavily in railroads. But because the South had so much slave labor at their disposal, they tried to build canals to match the North, as that was more economical. They took quite a bit of time to realize that canals were a stop gap technology. Railroads should have been the real goal from the outset. By the time they realized that... it was too late.

So the reason canals were more successful in the North was not because the South had slavery. In fact, for what we now realize were reasons of their own, slaves would prove to be some of the best canal diggers the world had ever seen. Putting canals in places that were seemingly intractable. And they died FAR less than natives or immigrants to boot. No... the reason canals were less practical in the south was down to geography. The reason the South believed they could conquer that geography was slavery. And the slaves were, for a variety of reasons, ALMOST able to pull it off... but in the end... physics is still physics. And many southern canal projects didn't work out as well as their backers hoped. (They didn't work out as well as the slaves had hoped either. But the slaves made judicious use of those that did.)

I always thought that if the South had invested heavily in railroads as soon as they identified the threat that the Erie Canal presented in the 1820's... they would have done far better in the Civil War. They probably still would not have won. They would, at least, have beaten the North's Eastern Armies, which looked pretty and marched well... but were fairly inept. The South and the North EAST would, in the presence of more southern railroads, have been evenly matched. The problem was... the North's Western Armies were hyper-competent. Far more capable than either the Eastern or the Southern Armies. Grant's guys were, well informed, (Pinkerton made sure of that), and REALLY meticulous about infrastructure. So I doubt railroads would have made a difference once the Western Armies were let off their leashes. But the South could definitely have performed better in the War. They may have held out a bit longer at a minimum.