I’m asian and grew up in Asia cooking rice without a rice cooker. This is how we do it:
1:2 rice to water ratio
Wash rice
Put rice and water in a sauce pan(?) or whataver you call that pan with deep sides.
Turn on stove to high heat until water boils (This is the initial 5-8 mins)
Once boiling, turn down heat to low and simmer for 40 mins (for brown rice. White rice is 20-25, broken rice is 12-15)
If I was to boil the rice for 5 mins and throw the water out, that means I need to boil water first (5-8 mins), throw in the rice and wait 5 minutes, then throw out the water. Only then will I do the above steps. The fresh water needs to boil again (5-8 mins) before I simmer for 40 mins.
Good point on heating the new batch of water while doing the initial boil. I can’t say I’ve ever cooked rice by throwing it into already boiling water though, so we’ll see how it turns out.