A significant part of medicine went down the road of finding specific tests which identify specific issues. We see this with cholesterol, blood sugar, numerous types of antibody, etc.
But there is a lot of sense in asking what can be measured, especially if it can be done simply and cheaply, doing as much as you can, then trying to establish its meaning.
Full Blood Count (called Complete in some parts) seems about halfway. Quite a bit of what we now see reported is the result of intensive automation of the analysis. In that sense, once you have gone as far as getting a sample and putting it into a machine, do what can be readily achieved.
Wristband devices have huge potential. One example relevant to my area of interest. In thyroid disease, the main tests are TSH, Free T4 and Free T3. If all three appear within reference intervals, patients are often told all is well. Which is simply poor medicine and statistics. There is generally greater variation between individuals than within. Our personal reference intervals are much tighter than those of the population.
Adding other factors might make a huge difference. It might look sensible to consider temperature, heart rate and oxygen saturation, but we really don't yet know what will have real benefits.
And I'd like to see a mass of simple factors put into them analysis system. I know many ask for weight and height. Try adding in foot/shoe size - length and width. Finger lengths. Breathing sounds. Vocal capabilities.
The further we go, the more relations we'll start to appreciate. Which will also provide individual base states which will inform changes due to other diseases.