Slave labor economies kill themselves because they destroy the class of small holders and small craftsmen--this can be seen in the effect of the latifundia
on the Roman Empire. Small holders cannot compete with the large, slave-driven agricultural operations, so that small holders eventually sink into abject poverty, or they get out to find land elsewhere (this can be seen repeatedly in the history of the American South before the civil war). Small craftsmen, even though they often produce a better product, cannot compete with slave labor--plantation owners often used slaves for smithing, carpentry and other skilled or semi-skilled trades, and they "lent" their skilled slaves to other plantation owners. The alternative for small craftsmen, whose only market was other small craftsmen or small holders, was to sink into abject poverty, to get out to sell their skills elsewhere (this was seen repreatedly in the years before the war).
You don't have to feed, house and clothe machinery, you just have to supply either the steam power or the electricity. But you do have to feed, house and clothe slaves if you expect to get useful work out of them. Even when you get useful work out of them, it is given without enthusiasm or a care for the quality of the work done. It is a very poor return on the investment of feeding, housing and clothing the slaves.
Furthermore, slavery served monocultures--growing tobacco or growing cotton. Both monocultures exhaust the soil, which is why plantation owners in the South switched from tobacco to cotton after Whitney invented the cotton gin. But, of course, cotton eventually exhausted the soil just as tobacco had. The lust for new land seen in the south after the War of 1812 was in order to use slave labor to clear new land and plant cotton. Having exhausted the soil, they would move on, or attempt to move on. The South had thought to continue that pattern with new lands acquired in the Mexican War, but it didn't work out as they had thought it would.
There was also a characteristic peculiar to the culture of the slave estates in the South, and that was the application of the law of diminishing returns in their foreign exchange. Long, long before the United States existed, southern planters had established relationships with mercantile houses in Europe, who would receive the tobacco (and later the cotton) and ship back manufactured goods--goods often of an inferior quality and offered at larcenous prices. Washington saw this, and got out of the tobacco business and diversified his crops to produce harvests which he could sell in the colonies (see the biographies of Washington by Freeman and Flexner). Contrary to a persistent historical myth about the United States, the slave economy was not responsible for economic growth in the United States. The foreign exchange produced by tobacco and cotton went right back to Europe for manufactured goods, while southern states fought the tariff tooth and nail in the Congress. The foreign exchange did not produce capital which circulated in the economy. By contrast, the foreign exchange received in middle Atlantic and northern states for grain, livestock, beef and pork, hides, leather and lumber produced foreign exchange which then circulated in the economy as investment capital, and the northerners bought their manufactured goods from American suppliers--which is why they fought tooth and nail in the Congress for
Your view is naive and simplistic and demonstrates ignorance of or a shallow understanding of the economic realities in the United States before 1865.