LOL, an investigation of what? A rumor that there's a child-dungeon in the basement of a pizza parlor that doesn't have a basement? Your delusion that if someone who owns a pizza parlor mentions bringing pizza in an email exchange about plans for a party they're really talking in "secret code" about child-slaves?
The nonexistent basement under the pizza parlor wasn't just some "mistaken belief" on the part of one person. It was the central setting of the whole PIZZAgate fairy tale. If there was no basement full of victims - if you determine that the alleged crime would've been physically impossible to commit because the crime scene itself factually doesn't exist, what's left to "investigate"?
And that is the other biggest failure of pizzagate aside from its nonexistent crime scene, is the lack of actual victims. If I call the police on my neighbor saying that I suspect for x, y, and z reasons that he is abusing his 10-year-old daughter - see, there's an actual alleged victim there. A real 10-year-old girl with a name and a verifiable existence, who might be getting hurt; without one of those, there's not really a crime to investigate. I can perhaps extend this requirement to police officers posing as children in order to ascertain intent - but pizzagate doesn't even have that. Pizzagate's victims are nothing but MacGuffins; nameless, faceless "children" of indeterminate age and number, as many as the conspiracy theorists want to exist. They have no origin - "kidnapped" from nowhere in particular, conveniently reported missing by no one. Maybe police would've had a little something to go on if the pizzagate morons had identified an actual known-missing child that was supposedly being kept in the dungeon.