There is nothing stopping companies from hiring freelancers from Latin America, without adding another middleman (like your service) which will, of course, cost something.

Having tried this setup and having dealt with middlemen (eg. Pilot) and not, I can't say I noticed much difference with dealing with self employed.

Especially if the team members are senior, they're likely to know the ropes of setting up business in their country.

That said, hiring from Latin American has its challenges - the language barrier is not easy to overcome and the political instability can take a toll on your friends and coworkers (especially in these trying times).