But going back to Theranos, I believe the problem they ran into is local variance: when you analyse tiny amounts of blood, two samples from the same blood draw end up with very different measurements for some quantities of interest. You just need a larger sample and that is a big problem for Theranos.

I think that's an issue but Theranos tests don't need to match existing tests in accuracy to be useful in a clinical setting.

Both blood to be drawn from veins and money are limited resources. If Theranos can mange over time to test two orders of magnitude cheaper on both resources then you circumvent the problem of local variance by testing multiple times. Testing multiple times has the advantage that you can circumvent temporal variance as well which current testing procedures don't do well. Multiple tests also give you data about the local variance and the size of the local variance is plausibly a clinically relevant number.