I work in Australia, so it is probably vastly different, but here are my experiences (other Aussie Ops, if you'd like to confirm or disagree):
We work as a subcontractor, and therefore have to have our own Public Liability Insurance to cover ourselves. If we were instead employees, we would be covered by the production's Public Liability, as well as their Work Cover (employee injury health & income insurance). $5-10m is standard in Australia.
Insurance for our own equipment is our own choice - sure, we don't have to insure it, but what happens when you take a fall..? Productions haven't asked for that, though they have required all my mains power cables to be tagged & tested.