Physics can tell you how frictionless, spherical cows behave in a vacuum. When you see real cows behave differently, you can investigate which of your violations are violated (and by how much, and which assumptions are still ok to make; eg air resistance is seldom a factor in the movement of real cows). The spherical cows are still a good starting point.
Economics can be similar. First, I doubt that staffing companies are actually all that profitable across the board. Yes, the difference between what they charge and what they pay out might be big, but they have plenty of overheads. Do we have any sources for their supposed extreme profitability?
Second, I suspect that any remaining excess profitability can probably be explained by barriers to entry.
Though some quick googling really makes me lean very much towards the first: staffing companies are by and large not more profitable than companies in other sectors.
That seems weird. Why would they be extremely profitable? Are there big barriers to entry?
Without barriers to entry, you would expect the profits of staffing companies to be competed away. (Just to be clear: you wouldn't expect workers to be less exploited. That's a feature of the visa system and their relative lack of other opportunities, not a function of the staffing companies.)
If there are so profitable, why isn't everyone and their mom starting staffing companies?