States vary as to how effectively they run their alerting systems, and how well they follow best practices, but that is ultimately an issue for the voters.
In my own assessment, I classify that person to be dangerous. A stranger takes a child for an unknown reason. A parent takes a child, willingly harming the child physically or mentally in hopes of doing harm to a person they hate. I would assume they are willing to do far more than mere mental harm to the child, if it means "winning" the fight. I don't have any data to back that up, and it's entirely possible I'm wrong. I just don't see an Amber Alert being raised because a parent took the child to be any less serious than if a stranger took the child.
I would imagine that some number of Amber Alerts are a kind of "false positive", something like failing to drop a child off on time (out of gas, severe traffic, etc.) and their phone dying, turning into a big ordeal, but I just wouldn't discount the situation just because the suspect is a parent. Maybe that shouldn't meet the threshold, but I just personally don't see it as being a big enough nuisance to be bothered by it. Again, it is easy for me to say that though, since I don't get those sorts of alerts very often, maybe 2 to 3 times per year, if that.
I do also completely agree though, that as it relates to headphone usage it should be changed. I think that if you are listening on your headphones, it shouldn't come through your headphones at all. Just play the noise on the phone speaker - it'll probably still draw the users attention. I might be asking too much though, as there was that 911 bug [1][2] a while back.
[1] https://news.ycombinator.com/item?id=29492884
[2] https://old.reddit.com/r/GooglePixel/comments/r4xz1f/pixel_p...