I'm currently working as a subcontractor for a friend's consultancy. For the better part of the last decade, that consultancy relied on remote workers (outside the US) to generate margin.
In that last decade, my friend has discovered there are costs with a remote-only development team and so has decided to insource technical, marketing, and management roles. Her clients are SMBs in the US, and business is growing.
So, one direct answer to your question about how a US freelancer can "compete with wages set at the global standard of living, including currency exchange differences" is to serve a US clientele whose products and services are closely tied to the US and (in my particular case) where being in the same time zone has a significant impact on getting work done.
I'll also add that the insourced group is implementing more reliable processes and producing higher quality deliverables to the consultancy, as measured by client satisfaction and owner feedback.
EDIT: Add paragraph regarding work quality of insourced group.