Yet, you find lots of uses for measuring stove and stack temperatures and will measure draft using instruments when there is reason to do so. Those are both elements of combustion analysis, and both would vary in results depending on species of wood being burned, how the stove is operated, where you are in the burning cycle and so on.
It seems to me that measuring the level of oxygen and carbon monoxide in flue gasses, for example, would provide useful information on how complete combustion is in a stove. At least for measuring oxygen levels, there are ways of doing that at moderate cost. I have a carbon monoxide meter I used during my days as a gas appliance repairman, but that limits out at 2,000 ppm, probably too low to be especially useful for measuring problem situations in wood stoves. But there is such equipment good to levels of 40,000 ppm ---4% carbon monoxide gas.
I've used meters that measure the level of explosive gas in a sample provided. I used that equipment for inspecting for underground gas leaks. IAs I think about it, it might be useful for detecting levels of carbon monoxide (an explosive gas) below at at the lower explosive limit of carbon monoxide). That might be a useful instrument for measuring CO in a wood stove flue gas sample ----I'll have to investigate that further.
And you don't necessarily need to modify a stove to change the combustion going on in a stove. Defects in the stove or repairs needed in the stove might cause problems with combustion, the fuel being used, the way the stove is operated and the venting system can all affect combustion. At present, you guys are measuring stove temperature and draft to help identify issues like this that need attention. I merely suggest that perhaps additional methods of combustion analysis might prove to be useful in the same way if they were tried.
I'm interested in finding the people who have tried out such equipment and perhaps use it when there is good reason to do so. Or perhaps they have tried it and found it of no utility, as suggested by those on this board. But you really can't have an authoritative opinion on the subject if you've never tried it,.