I am aware of this... but it actually doesn't work well because the calibration adds a large amount of unnecessary error.
When high precision is needed the rider is doing A-B-A-B runs, switching between configurations. In this scenario, it is not so important that the calibration be accurate, so long as it is not different for A vs B. If the airspeed is off say 2% from reality, it will be off 2% for both. If on the other hand the change in configuration necessitates recalibration, calibration accuracy becomes extremely important, since it will directly affect the results.
I assume that calibration is performed by making the assumption that the wind vector relative to the ground averages for out-back runs? In other words you say that the wind does not have a bias. But how many runs do you need to perform in order to have confidence in this assumption? I can tell you that on a windy day, the wind varies a lot in direction and intensity. On a single out-back you could easily have 2mph net headwind or tailwind. How many runs would you need to "cancel" it out to a reasonable level of confidence where it doesn't impact your result? We are typically interested in resolving to CdA differences of 1% or less. The calibration error would need to be much less than this to be "acceptable". Maybe 0.25%? The wind error that would result in a CdA error of 0.25% is only ~0.1%. If you are testing at 30mph, this is 0.03mph. That ain't happening! Even if you are out there all day going back and forth you are not going to reach that level of confidence in the "wind canceling" assumption.
Regarding the "wind canceling", I'm already setting a wind vector when I do my analysis, with the assumption that the wind cancels out. I'm currently varying it with each run; wind cancels for each run and I average the CdA results. It would be better to have a global constraint of wind canceling for the whole test rather than each run, but I kinda suck at spreadsheets and am even worse at programming, so I haven't bothered. But if I did that I would acheive nearly as good results as the Notio... without measuring wind at all.
So, no... recalibrating won't work. The calibration needs to be stable for any changes you make in configuration.