We use Justworks and they do that all for us. You're technically an employee of Justworks, and their name shows up on your paychecks. You hook into their health and 401k benefits, and they check all the workplace safety boxes. For instance, they'll mail you posters you legally have to put up in your office to ensure you're telling employees about overtime. HR plays literally no role in any of time apart from maybe selecting the health plans, something we do once a year and roll over every time.
> ensuring that staff is well trained for their role
What does an HR person know about training for your role? Is HR cross-trained in engineering for instance? Seems wildly different from my experience. HR would ineffectively screen candidates and ask you about buzz words. So they'll ask "do you have experience in Javascript" and I'll say "no, but I have a lot of experience in Typescript" and they'll just screen me out because they'll have no context.
And HR staff is also much more social so they'll pick up on awkwardness and screen there as well, when in many fields like engineering, the tolerance of awkwardness is much higher.