I have done 2 different house sits in Australia and both insured their car for us. One offered it in their listing, the other, we just asked and they didn’t hesitate in saying Yes.
I had to say no to a HO recently due to another accepted sit. She was very offended that I hadn’t checked in with her first! I loved that sit and hope to go back but it was funny that she thought she was the only HO I knew!
I only choose locations where I can travel low cost. Sometimes I even bring my own food (Israel is way too expensive for instance). Small cabin luggage so flights are cheaper and it is easier to move around. I started last May with THS and till the end of the year I did 9 sittings and turned down 5 more because a) dates conflict or b) flat was not that great.