The field sobriety tests is designed for catching alcohol. 2 out of the 3 tests in the link you provided specifically say that failing them is associated with having consumed too much alcohol. The only one that doesn't specifically state as being about alcohol still only tests for a very specific impairment common to being drunk .
Is it your position that it's impossible to determine impairment if it isn't alcohol related?
It seems to me that it's the skills required for safe driving that are at issue, and if those are impaired, there's a problem. If not, then it's not an issue (at least not with driving, which is what we're discussing).
I imagine it wouldn't be too hard to modify (if necessary, and I'm not sure that it is) sobriety tests to cover those skills (e.g, reaction time, coordination, object recognition, etc., etc.) and make a pretty good assessment of the subject's ability to safely operate a vehicle. If there's a positive result, further (blood, saliva, etc.) tests could be performed to confirm the result.
This would save time, money and, in many cases, stop needless invasions of privacy (e.g., forced body searches -- which breathalyzers, etc. are). I'm not sure what your objection to field sobriety tests might be, unless you work for a company that sells onsite testing kits. Please elucidate.
I used the NHTSA test regime as an example, not as the definitive test that must always be used by everyone, everywhere, for every test.