"Yes" is not an answer that should be responded to. Details are what should be responded to. Cops shouldn't be asking the neighbor's approval to investigate. They should treat a report as a witness, and refer to a checklist of types of observations that need to be investigated.

If a neighbor makes up details in a report to police, they should be charged with a crime. If the cops are asking "do you think we should investigate" to private citizens, they have abandoned all responsibility as law enforcement.

Imagine crowdsourcing your authority, making the justice system a militia for lazy mobs. Completely upside-down.

I agree. The problem is that police in much of the US are poorly trained, poorly funded, poorly managed, and increasingly marginalized. The US system of strong local governance means that only the nice neighborhoods get nice public services.