I was told long ago that the water was needed to support the stalks (over the last 20K or so years humans have engineered edible grasses to have absurdly large seeds).
Definitely not the case. At least here in Japan, right now the seeds are large, but the fields are mostly not flooded. I believe the reason for flooding the seedlings is to crowd out weeds, which unlike rice are unable to get established.
Bali has reliably warmer weather than the Riverina in the winter months, so at a guess insulation would be less relevant for Balinese farmers.
[0] Australian rice growing is good for comparison because it necessarily has to be more water efficient and is more heavily industrialised than Indonesia
Not sure where you heard that. Everything I've read (and a quick google search to confirm) indicates that rice fields are flooded because it's a cheap way to prevent weeds and pests from destroying crop yields.
Historically, that may have been an issue. But modern ("Green Revolution") rice varieties are mostly dwarf or semi-dwarf, which plausibly reduces that need.