We already have a system for that it's called Handheld Remakes or something (can't check right now). Electronic Game & Watch simply makes no sense at all, if people are using it for all handheld games then that's their problem, but we can't consider this a standard name because it's plain ridiculous, same as calling a system Nintendo Game Gear.
If you don't like Handheld Remakes you can use Electronic Handhelds instead. I kinda like remakes because most of these are actually simulators not emulators, we can have both system names though. And in the future due to the latest MAME progress on this I'll want to have separate systems for LED,VFD and LCD games since they are very different from each other so for this purpose Electronic Handhelds wouldn't be a bad name.