In some countries, there are rules requiring that you report and/or withhold taxes on behalf of the contractor to the local country they're working from. This can introduce an administrative hassle for you to comply with international tax laws, even if you're just working with someone as a contractor and not a permanent employee.
Contractors can make it easier for US companies to work with them by setting things up in certain ways on their end (I'm being vague because this really varies per country). For example, in my EU country I started a limited company and received a special tax status which tells my tax authority that I alone (not my contracting client) am responsible for all tax payments and reporting for my work, removing that burden from the US-based client.