In our business the health and safety team has a budget of $0. Each business unit is expected to pay for health and safety costs out of their own operational budgets. We can make recommendations for training training or equipment but since we have no financial authority it's not up to us to make it happen.

Hi Michelle
Slight correction in your first sentence - PCBUs must take reasonably practicable steps, not all practicable steps.
From my limited knowledge - We have effectively the same, a budget of pretty much $0. H&S costs are part of the cost of doing business, but once accountants get involved, those costs get allocated to individual departments in the same way that operational training, administrative overheads and maintenance costs are allocated.
If your organisation has an appetite for it, you may be able to itemise (ie create a budget) organisation wide H&S items. I'm thinking purchasing Standards, subscriptions to Safeguard, external audits, D&A tests, your salary, phone, computer etc. Maybe talk with your accountant to see where those demarcations lie.