> But in practice, I greatly prefer devices with integrated batteries, because they're more likely to be able to give me useful feedback about the battery level (e.g. a reliable low-battery indicator), rather than just winding down, or having a low-battery indicator with only a passing correlation to reality.

That has less to do with the battery being integrated and more to do with different battery chemistries having different voltage curves.

Nothing would prevent a device from accurately detecting battery levels of NiMH batteries. The problem is all these devices are tuned to an Alkaline battery voltage curve which is much more slanted than NiMH. NiMH has a nearly flat curve with a sudden drop off while Alkaline have a pretty steady decent (with a sudden drop off).