This is not true for all flights to/from Canada, of course, but it does add complexity, expense, and often travel time for people who want to deal with Canada while avoiding US authority.
Overflight of US airspace doesn't give the US authority over the people inside the airplane. And flights to Canada from Europe or Asia don't overfly the US, except perhaps Alaska, but that's of zero consequence.
You're right that many direct flights between Canada and Europe or Asia don't overfly the US. Many of the affordable options are via US connections, however, and travelers from the rest of the world to Canada frequently overfly the US.
As for Alaska, it's very much a part of the US, to the level that everything I said above is true for flights which only overfly Alaska and none of the rest of the US.
Is it possible that some people are afraid of being charged with "Conspiracy against the United States" [1] and that they have to wait a long time in the USA until a jury decides that they are innocent?
[1] https://en.wikipedia.org/wiki/Conspiracy_against_the_United_...
It's unclear (and doubtful) whether that is true:
"All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside."
Courts could probably use the jurisdiction language to say "nope". No idea whether there have been any court cases over this though.
I'm not sure whether it's due to a specific law, or courts applying 14A, but there's broad agreement that babies born in US airspace are, indeed, US citizens.
In practice, what I said above is well-settled legal and administrative practice in the US, whether or not the constitutional words could have been interpreted or differently by Congress and/or the courts.
US authorities receiving proof of birth above the US and lacking reason to suspect parental diplomatic immunity certainly will and actually do grant proof of US citizenship, no further argument needed once the location of birth is documented.
For example, as an American who lived in the US for more than my first 30 years of life, any (biological) kid I have anywhere in the world will be a US citizen by birth, regardless of location, based solely on US law, even though outside the US I'm generally subject to the host country's laws and not to US laws. (Nationality laws are not the only US laws to have extraterritorial application, but the default rule is for US laws to apply domestically only.)
As an inverse example, the denial of US citizenship by birth to people born in the US to two diplomatically immune parents is solely due to US law, not due to any international agreement, even though the diplomatic parents are mostly immune to US law and subject to at least a large fraction of their home country's law.
Here's a general Wikipedia summary of how birth aboard aircraft and ships works for purposes of nationality, including specific comments on Canada and the US, as well as addressing the two international conventions that people often think are relevant to this question but aren't: https://en.wikipedia.org/wiki/Birth_aboard_aircraft_and_ship...
The US nationality rule for birth outside of the US is narrower than "anyone with one US parent", by the way. It wouldn't apply to cases like mine if my time spent living in the US had been below a certain threshold. By contrast, even children born in the US to those whose presence in the US is unlawful or otherwise irregular are citizens by birth.