This will be done more and more until the first crash. Then everyone will freak out and everything will be grounded. The engineers will point out that statistically the flights done this way were safer ( 1 million miles were flown by AI in the last 3 years with only one incident. The same done by commercial pilots would have caused 3.5 incidents!)
Then other incidents will be dredged up. Some won't be actual incidents, some won't be the fault of the AI, and some will be because a human overrid AI control. However, the public will firmly be on the side of only humans should fly planes. Laws will be drafted. Then loopholes for "drones" will be made. A decade later these loopholes will be large enough to fly a 737 through.
No one will remember why they were put in place in the first place, but one political party will be firmly against removing the laws. It will take another generation for them to finally be removed, and by that point computers will be so far integrated with humans that biological humans might be banned from flying under the law if things didn't change.
Hopefully, people will look back on this and say, lol, no, that post was edited in 2035, but good try.