Hmmm.
The GNR and associated S & R entities did search for her as best they could, trying to adapt their training and experience to an unusual situation.
The PJ clearly suspected the McCanns / T7, but also followed the "lead" concerning Murat, which led nowhere.
Then... they were stuck. No obvious forensic leads (they didn't have a DNA database anyway), nothing they could actually pin on Murat, no national sex offender register... and so it was no doubt easier to go back to assuming the parents were involved and concentrate on that.
They didn't have a crime investigation manual to assist until sometime in 2009.
Shoe-horning had worked in the Cipriano affair, the only other case of a missing child that the lead investigator with 27 years of experience had worked on, but slippery stairs weren't an option this time.
The propaganda machine was the only weapon (and that was used extensively in the previous case, with effective results in terms of securing a conviction).
To this day, anyone questioning the lack of evidence or the absurd theory in the Cipriano case gets branded as a child-murderer supporter, so the propaganda machine clearly did work.