As a rule police do generally have an idea as to what has happened, and often do cover all ground until they reach the conclusion they’ve been aiming for.
But in this instance it really does seem they don’t have a clue. They seem more and more to be clutching at straws with clearly very little to go on. And yes, I realise that not everything is revealed to the media, but they have been jumping from one theory to another, without even having any evidence.
“Random abduction” really does sound like “we don’t actually have a clue.”
TBH I don’t think many sightings in these cases have any credibility. There’s a reward on offer, people will report seeing any child with the same colour hair/build etc and then say it’s a sighting.
When Madeleine McCann went missing there were hundreds and hundreds of so called sightings, and even MN’ers who said that they had been approached by strangers questioning who their child was. And on the other side there were MN’ers who posted that “I saw a blonde child who looked very like Madeleine at my local park/soft play/the supermarket,” and others were urging them to call the police “after all, if it’s innocent then the parents won’t mind, but you could possibly help save a child.” Bloody ridiculous IMO but it’s not uncommon.