> Police in the US simply need to be equipped with roadside chemical tests for substances. They exist, they just simply don't use them.
I feel like you're not getting my point.
> Doesn't that sound like a better solution than: "The officer makes you stand on one leg and say the alphabet backwards, if they don't like they way you did it, you are charged with DUI"?
No, it doesn't. DUI isn't a law that lists a bunch of chemicals that are illegal to drive while using. The purpose of the tests is to prove you shouldn't be driving, not what drugs you're on.
You could be over-tired and get a DUI and I think that's justified.
Are you sure about that? Maybe your locale is different, but the DUI/OVI statute in the part of the US where I live is for influence of "alcohol or drugs" specifically. And it absolutely does have a list of what qualifies... and that list basically includes all drugs and alcohol.
Part of the criminal element of DUI is someone's choice to alter their body intentionally. I don't think many would think it would justly apply to natural processes like sleepiness or medical emergencies. That's not to say there shouldn't be penalties for failure to operate a vehicle safely, but those situations are clearly very different than DUI.