Jeff is correct. A lot of birds covered under the migratory bird act are hunted. There is a waterfowl season and many migratory birds land on the dinner table! Even in CA there is a crow season. Dec 5 - April 7 - daily bag limit 24 crows.
https://wildlife.ca.gov/Hunting/Nongame-Furbearers
The main issue I see is that people confuse crows with ravens and then get in trouble. I have never tried to hunt crow, like others mentioned, they seem strangely absent when there is any hunting going on.
Personally I don't care for the crows at all, mainly because they come through my area a couple times a year in big groups of 100+ and systematically clean out all the song bird nests. Air battles ensue with little birds trying to fend off the crows ...
G