Theory: They had some early tech that looked promising in some specific clinical circumstances that through dumb luck were the ones that were tested early on. Holmes, as an almost engineer with no particular experience in anything, thinks medicine is just like engineering. It didn't work in the general case or was less accurate than acceptable for medicine, and so now Theranos is basically just doing normal lab tests…
Most blood tests, though, are about detecting whether levels of a substance are in a particular range - milligrams of cholesterol per deciliter of blood, mg glucose per deciliter, etc. Taking a much smaller sample is pretty much guaranteed to make the plus/minus error range larger, and capillary blood from a finger prick will have a greater percentage of contamination from intracellular fluid.
Even glucose meters you can use at home are much less accurate than glucose readings taken with a venous draw in a lab. In that case, the benefit to a diabetic of being able to do frequent home testing outweighs the loss of accuracy. If you're going to get work done by a lab, though, you are going to want it to be as accurate as possible, and in that scenario I don't see how a finger prick will be able to compare to a venous draw.