What incentive does an institution have to hire expensive research staff instead of having PhD students fill all those roles? I don't understand why a research institution (that awards PhDs) would employ (expensive) full-time research officers. Why couldn't those jobs be done by a group of government-funded PhD students instead?  (The PhD students seem to be free or at least less expensive to the institution.)

No funding? Simple, just hire more PhD students! They can do whatever the institute requires them to do, such as publishing X number of papers. They are smart but cheap.
A PhD is where you learn to do research to a doctoral standard.

A research job is where you apply what you've learnt.

These things are different things. They are not the same thing.

It's like why you see a qualified doctor instead of an undergraduate studying medicine.