"I have ground speed and track from GPS and airspeed from a pitot tube then I can calculate the ambient windspeed and direction"
Right, but it is not the same as getting airspeed from GS, since in that case you have to get GS(gps velocity), last wind readings and you have to have a really nice INS that would give precise enough acceleration measurements (not INS for 150$) so that when you feed all that stuff into some sort of soph. alg (kalman filter or smthg), you would get correct(more or less) "airspeed" reading.
In the lab that I am working in (university lab - aerospace/engineering dept) we got INSsa that cost 10 times as $150 and it's not as precise for supporting that kind of model of obtaining airspeed as it should be.
What I was arguing about is -> $150 might not be enough.
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"If the pitot sensed airspeed drops out"
caution - conditions that determine that "drop out" might be vague.
It is probably easier to let this thing to be decided by a pilot.
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If am not mistaken, at least B787 have that mode in which it derives airspeed from gps and (I am assuming, by using INS too). In that video the difference in airspeed and calculated "airspeed" was around 5 kts. But, again - not with a $150 solution )