Yes the EC can arrange insurance, (the SM works for you and has to do what you tell him, if he doesn’t like it get another SM).
Yearly insurance valuations seems a bit much (QLD once every 5 years). You need to check reg in NSW.
OH&S is my pet hate, we have the same in QLD. It’s Workplace Health and Safety and as far as I’m concerned a small residential Stata is NOT a workplace. How often do non strata properties (homes) carry out one of these (never in my experience). I can understand large residential / holiday lets with onsite managers, lifts, swimming pools etc requiring this but in your sit noway.
I found this on NSW H & S website
A strata title body corporate responsible for any common areas used only for residential purposes is excluded from the definition of a person conducting a business or undertaking (PCBU – the new term that includes employers) under the Work Health and Safety Regulation 2011 (WHS Regulation) unless the strata title body corporate engages a worker as an employee.
https://www.workcover.nsw.gov.au/newlegislation2012/Pages/strata-title-body-corporate.aspx
Seems to me your SM is ripping you off left, right and centre.