It seems to me that there are two different illnesses here: T2 and T1. While they may have the same symptoms, the causes are very different.
T2 appears to have a very strong genetic link, combined with a nutritional element. Plus I've never heard of any non-obese kids getting it, so if I were a T2 parent I'd be spending my energy on encouraging appropriate (not high carb but no need to go keto) diets for my kids, and ensuring that they aren't obese. (Still not sure whether obesity is a cause or a side effect of T2, but in either case avoiding poor food choices such as sugary sweet drinks is a good thing.)
As a T1 parent I've never blood tested my (now adult) children, but I did use to test their urine on the rare occasions that they were extra thirsty. Given that you pass out sugar in urine once your blood sugar goes over 10, that seems like a good early warning system which doesn't stress out the children. (And honestly, I think I had occasion to do it less than half a dozen times during their childhoods.)