Yes, it gets sent out to every phone in the target area, it also gets broadcast on radio and TV channels.

Sure, the person of interest will get the amber alert, but realistically, they probably know that someone is going to be looking for the kid sooner rather than later.

And while 400km (about 250 miles for other Americans like myself) is certainly a big area, that might be only like 3 or 4 hours of driving if they take major highways. I know people who regularly drive double that in a day and think nothing of it and they’re not even trying to flee from a kidnapping.

And of course, there’s probably going to be some time delay between when a kid goes missing to when the alert gets pushed out. The parents/guardian may not notice right away that the kid was missing- maybe the kid was playing out in the yard while they were inside cooking dinner when it happened, they may spend some time looking around the house/neighborhood and calling everyone they know before calling the police (I work in 911 dispatch, the amount of calls I get from some friend or relative in another state because the person having an emergency called them instead of calling us never ceases to amaze me,) and then it may take some time for the police to get out there and collect the necessary information and go through whatever process the area has for issuing the alert

So it very well may be a few hours since the abduction occured before the alert is issued.

And of course, like you said, they do try to determine an appropriate geographic area to issue the alerts in, if the abductor is known to live 400km away, or has made specific threats to take the kid to a certain location, or there’s other reasons to think that may be where they’re headed, it seems pretty reasonable to me to alert that area and much of the area in between the two locations.