At my org they also organize the Thursday evening drinks session :)
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.
IME they don't know anything about the training itself. But they don't work in a vacuum, so there will be training programs set up by "regular" staff, and HR will make sure that you have access to them, that you attend your training if it's mandatory, etc. They'll also ask you if you need any kind of training you're not getting, and figure out a way for you to get it. Again, this usually involves the "technical" staff. They're typically facilitators.
This is what I've noticed in two medium-sized companies in France.
An example from companies I've worked out is that they make a matrix of competencies and job functions to determine what knowledge (e.g. specific skills or specific business knowledge) is required for particular functions. This isn't there to veto hires because of a buzzword they miss - that would indeed be terrible HR and does happen; it's instead there to structure onboarding, trainings, etc.
Not everybody on the IT team needs to have deep understanding of the billing process, but some do, and the same goes for some support roles and other functions. That means for certain sized organizations somebody in billing needs to have a well-documented overview of how things work, and regularly present it. This seems obvious but for an org that grows from 30 to 100 people it's (somehow) not always so.
Similarly something as simple as saying "Who in the organization needs to be able to present things at a high degree of clarity?". I'd go so far as to say the org NEEDS them to have followed a 1 day training course on how to present properly for their function. It just saves everybody around them so much time and work. Does the receptionist need that? Every support engineer? Every Dev? Maybe, but probably not, but some do. HR defines those capabilities with the org and makes a plan to ensure it happens.
Bad HR definitely exists but it can be done right.
Mostly true for big companies in the US as well.