Running the bath for little kids? Most people are very careful about staying in the bathroom while the water’s running. As kids grow older (and safer around water) we relax a little and I certainly remember starting the bath running and then wandering off into another room to sort out some laundry or something similar… This is fine once all your kids are old enough to be safe around water.
But always always run the cold water first and add extra hot water afterwards. I remember, many years ago, going to the home of a family where the bath was run really hot. Mum was just about to go back to the bathroom and add more cold water but the 8-year-old beat her to it - jumping happily into the bath - and the skin all over her back, stomach and legs didn’t even blister… it just peeled right off. Fortunately Mum did exactly the right thing and put her straight in the shower under cool running water until we got there, but I would imagine that little girl still has scars. And her pain was just dreadful to see.
Always run the cold water first, then the hot, and then a little bit more cold just to cool the spout. I’ve burnt myself on the hot spout before now.
And make sure the water which comes out of your bathroom taps isn't too hot. Your hot water cylinder does need to be set at around 60 - 65°C so that the bacteria which causes Legionnaires Disease can’t grow. But a plumber can put a tempering valve into the system which means that the water which comes out of the bathroom tap doesn’t need to be nearly as hot as that (but you can still have hotter water in the kitchen and laundry if you want to). Well worth doing if you have little kids.