Outsourcing happens but larger firms repeatedly run into the issue that management, admin, and local talent provides diminishing returns. Most of the larger US-based firms have standards that are built on decades of developed industry practices, something that can sometimes be missing from outsourced workforces on a cultural level. Hiring in domestically at least plants folks in environments where they can learn those processes over time. I suspect this is one (amongst many) reasons why US work visas are so single-employer contingent - you don't want talent you trained from the ground up to be able to easily leave for another role somewhere.