> * Mitochondrial DNA is passed by mothers only and so undergoes very little mutation
It's true that mothers pass on mitochondrial DNA but this doesn't necessarily require the absence of mitochondrial DNA mutations. I would imagine the lower rates of DNA mutation are due to the importance of the mitochondrial genome for generating a cell's energy.
The ideal would be a rapid 'fever' panel that tests for all the viruses we currently pay a ton of money for. This sort of test could pick up early-stage HIV which, if symptomatic, don't feel much different from a cold/flu.
[1] - https://www.aafp.org/afp/2014/0215/afp20140215p265-f1.gif