Despite the enormous numbers of slaves in the Roman world, they made up a minority of the total population of the Mediterranean. Slave labor could never provide for all the labor demands of the Mediterranean world in the first place.

More importantly, the assumption that free labor and slave labor are interchangeable is not necessarily true, and overlooks a number of economic and social circumstances that complicate the idea that one laborer is simply equivalent to another in any given society. Free laborers and enslaved laborers did not overlap very much. You mention that it would seem illogical to pay a laborer at a constant rate when one could buy a slave. But the logic doesn't hold. For one thing, the Roman world knew no such thing as hourly wages, or regular salaries at all. The common, unskilled, unlanded laborer worked and was paid by day in antiquity, often at an abysmally low rate. The cost of a slave was large, and though the actual cost of buying another human being was a single-time deal, even the enslaved need clothing, shelter, and food. Slaves were an extended investment, an expensive form of labor that required a large amount of capital up front and then the means to keep one's slaves alive for years to come. By contrast, a hired free laborer can be taken on temporarily and, besides his immediate pay, is left entirely to his own devices. During busy times, such as the agricultural harvest, more laborers are needed than at slow times. Adding slaves is simply not an effective economic means of filling that gap--Cato expresses a preference for free workers during the harvest, because he thinks they work harder and because you're not stuck with idle mouths to feed during the slow season. There is every indication that slave labor and free labor simply did not compete with each other.

As a final note, the social realities of slavery really should not be overlooked. The threat of mass slave revolt loomed large in the Roman imagination, even though actual slave revolts were fairly rare. The higher the density of slaves in an area the more likely it was considered for an insurrection to break out. We know of several attempts to break up the ability of slaves to get together, and we can conjecture some others. The fear of increased numbers of slaves was constant in Roman Italy. Moreover, the social impact of free labor should also not be ignored. Vespasian, says Suetonius, rejected a design for some sort of machine that would have greatly saved in labor in construction, on the grounds that the urban workers who relied on monumental building projects for their livelihoods would be unable to eat if he accepted it. Had economic concerns been the sole motivation for any socio-economic action Vespasian would presumably have accepted it quite willingly. However, Vespasian lived in a society.