That's the service that an employer of record provides: they hire the worker locally and deal with all resulting payroll & tax complications, liability under local labor laws etc. while the US company pays a flat hourly fee to an overseas service provider.
Anecdotally, this is the setup I was offered for a remote job in an EU country different from the one in which I live. They didn't necesarily want a big company, either. They seemed fine with a company-of-one (there's no "freelance" status as far as my country's administration is concerned).
Whenever I was offered to work through Remote.com or Deel it was forcing me to be employed in their local branch as an employee. Which made the whole thing more complicated (higher taxation than on the direct B2B contract, etc.) and not so lucrative anymore.
That’s the point. You’re employed locally and do work for the remote company.
If you don’t want to work as an employee, then you can enter into a contracting relationship, but employers tend to avoid this because there’s always the risk that the local government determines the contractor is actually an employee and taxes are owed.