It depends. I worked at one company without a dedicated HR department (a payroll company) and it ran fine without it. Managers of each department worked with upper management and finance to decide staffing, we went to management and if needed (I never did) upper management or the lady who did our payroll (they handled both our payroll and client payrolls) or the benefits department (same deal) for most of the sort of things HR does at my company.

I think it's bloated at my current company, there are some people with not a whole job, but it's not like they do nothing or don't provide value, they do. But like, one guy's job is apparently employee development and all he does is choose some general "learning software" that we then have access to. Gives some useless and painfully boring presentations on the aforementioned software that provide nothing of value. Then I have no idea what he does with the rest of the year. Why is that one whole job, when the rest of us basically juggle multiple jobs?