Only happened because Union ships interdicted the market. In other words, as a consequence of the Union effort to control the South. Without the market disrupted deliberately by Union ships, those growers in Egypt and India would have never been able to compete with the Southern production. You can't beat free labor with paid labor. It ain't happening.
So again, to make sure we are clear on the underlying premise, the South would have acquired massive capital infusions from European trade *IF* the North had simply left them alone. Clearly the North did not do this, so the capital did not come, and foreign competition was allowed to get on it's feet when it would have otherwise been unable to do so.
You've got to keep your premises straight. You want to take the economic reality of what did happen and argue that this is what would have happened in an alternative timeline in which the South was allowed to go it's own way in peace.
The economic disaster for the powerful men in the North did not occur precisely because they used their influence with the government to launch a war against the South to stop it from happening.
Think Logically. Think clearly. Be objective.
Objectively, free labor stupidly executed, is not cheaper than low-paid labor efficiently performed. A slave picking cotton by hand is not cheaper than a wager-earner operating a harvester. The fact that the cotton gin made cotton a worthwhile crop in the first place shows that automation of labor works. But the South was unwilling to utilize the harvester prototype available at the time because it would replace too many slaves and leave them idle, which illustrates the weakness of the system. Ironically, the same weakness was on display with socialism, too. Both systems need the work performed to be as labor-intensive as possible, so efficient, cost-effective production is undesirable.
Egypt was not only closer to England, so its shipping could not be interrupted,but had an outstanding debt which they could only repay with cotton. When they failed to repay even with that, England cccupied Egypt. Were Egyptian peasants paid? Not much. Supply and demand kept the price of cotton low on the trading floors, regardless of how much it cost to produce and ship bailed, ginned cotton. And southern cotton was part of the supply even if they had no customers for it.