Substances found in blood are present at microscopic scale and tend to be invisible to the unaided eye. Why is a whole vial of blood (at ml scale) is required to assess the presence and concentration of substances, given that the modern equipments and testing is becoming more and more sensitive and efficient?
It might be better to consider the sampling technology, economic and logistical issues with this question as well as the tech behind the tests.
First, some tests still will want a few milliliters of blood - e.g. cell counts for specific cell types. Then there is the need to create and stock many different kinds of sample collection devices and train the collection centers to use them effectively- the industry won't be wanting to completely retool whenever the volume requirement for the assays changes.
Mainly, since the expense of collecting and shipping a few milliliters of blood is pretty much identical to doing so with a few microliters of blood, what has happened is that the tubes are used to do multiple assays with excess included in case an assay has to be redone.
Probably all this blood currently collected is not necessary at all. I expect that the cost of changing all the blood collection systems and protocols is not worth the cost of collecting the exact minimum amount of blood needed. The benefit to the patient or the lab between collecting 3-5 ml of blood and collecting 50 microliters of blood to be shipped off for lab analysis is probably close to zero.
Having more blood than you need does not hurt the lab either should they need to repeat the assay or when you need to use the sample for more than one different test.
@shigeta brings some other interesting reasons, but I think the main problem with small draws is lack of representativity.
I suspect you are hoping that something Theranos "nanotainers" will replace today's blood draws. The fact is, the first drop of blood is not the most representative for the whole blood. For example, drops of blood collected from finger pricks are not very similar. if they differ between themselves, they are likely to differ from the rest of the blood. This variability is probably why Theranos tests were shown to be quite variable.
For some tests, it might not matter. Home fingerstick tests for blood sugar at home are generally acceptable, but even those come with a warning that results are somewhat inaccurate. For others, such variability cannot be tolerated. They may be too expensive or too urgent to allow repeats in case of a borderline result. They may be so scary that false positives must be avoided as much as possible. In all these cases, the tests must be run in the most representative conditions.
More blood collected is essentially averaging multiple drops. Many tests are done on very small sample of blood - smaller than a drop. Drawing that sample from a bigger pool of blood makes the readings more representative for the rest of the blood.
There are hundreds of tests that exist but many require different technologies so getting them all out of one drop is nigh impossible.
For a large fraction of your average chemistry/immunology blood tests, the blood has to be transported in a way that keeps the blood liquid so the collection tubes have anticoagulants in them. The analysis involves pipetting microliters of plasma into a cuvette where different reagents are added and the ensuing chemical reaction is monitored by a spectrophotometer which detects various chemical products by select wavelengths that are absorbed or emitted. This requires the red blood cells to be removed before the sample can be analyzed(they would block the light), so the collection tubes have a gel at the bottom and the sample is centrifuged before analysis so that the blood cells get buried in the gel and the analyzer probe can then extract just the clear plasma above it. Each assay has to be run in it's own cuvette otherwise the reactions would all be mixed up and it wouldn't be possible to quantify the assays separately. Using this approach we can currently run about 50 quantitative assays out of a
ml or two of blood. Some assays require different kinds of tubes for various reasons so they may collect a red top and a green top tube when otherwise a single tube would do, and, as others have said, some excess is collected to enable reruns or add-on tests that your doctor may specify after seeing your initial results. If you only collected a small drop of blood (like is used in hand-held blood-glucose meters), you wouldn't be able to get it out of the collection tube and into the multiple reaction/measuring cuvettes.
There are technologies that detect e.g. DNA on a chip that could conceivably detect multiple viruses and things from a single drop of blood, but they fundamentally rely on some underlying chemistry/physics that would probably make them single use if connected to a phone. While they are very specific, that tends to make them good for detecting things qualitatively (do you have HIV or HEP-C?) but probably won't make them good for quantitative test (how much potassium or glutamate do you have in your blood). And trying to combine that with e.g. counting red and white blood cells is unlikely at this point. But technology is constantly improving.