The main reason we had travel insurance was for medical coverage, I never really thought of the non refundable component as I generally will not pay in advance. Pre covid our drill was simple it was to get Mrs & MissM rewards flights sorted, book refundable accommodation and then monitor for the refundable special/ location offers. Using this approach I have found that booking accomodation (refundable) around the 9, 7 or 4 months out seems to be the sweet spot and is often cheaper and better value than what the booking sites have on offer 2-4 weeks out. In saying this I have cancelled and rebooked with the aggregators if the savings were significant. As for my flight, I just wait for the routine sale fares be it QF, CX, JL or any other OW carrier when I thought the fare is reasonable (lowest) some times I was right other times I got it wrong.In regard to when to take the insurance, for an annual multi-trip, the answer partly depends on what you have pre-paid and whether you can get a refund/credit for amounts you have paid. If you are not at risk of loosing any $, then no need to purchase the insurance at this stage. However, once you expend significant, non-refundable $$$, you need to consider whether you would be happy to loose the $ or want them covered by insurance.
As we had rolling family insurance coverage many of the points that you raise are valid considerations and well worth a second thought given we are now starting from scratch, again.
I did not know that you could purchase TI once a trip has started, can a policy can be backdated and paid for, I have no issue with this I just did not know this was available.There is no 'required' time to purchase insurance. You can even get cover after you have left Australia and commenced your trip
As Jaques Vert points out however, cover only starts from the time the policy is paid. Any pre-existing matters at the time the policy is paid - whether health or logistics-based - will be excluded.