Companies have their own internal regulations, code of conduct, and cultural norms, and HR is ostensibly knowledgeable of these factors, as well as being trained specifically in employment law. Besides that, there are jurisdiction issues that HR aren't bound to -- e.g. if the alleged violation happened during a work trip to Kentucky or overseas, the complainant isn't required to travel to that court (or deal with the feds) to get the matter adjudicated.
But beyond that, I'm curious why you think the police are the gold standard for handling all of society's disputes? Again, let's ignore that the people and groups who constitute the "police" vary significantly depending on jurisdiction; and also, of course, that the police do not make the ultimate decision to press and pursue charges (that would be the prosecutor's office). The police have the power of government authority and protection behind their decisions and actions, but that is orthogonal to whether they are trained and equipped to come to the right and/or optimal decision.
It's no different than a company hiring private guards for security -- guards who are not only willing to do, well, guard duty, but also are familiar with the company's culture and regulations etc, and are (we would hope) specifically and better-trained for the attack vectors that the company faces. It would be absurd to argue, "Well, that company must not have real security threats if they didn't contract with the police to guard their workplaces"