This tragic affair shows why law enforcement should not be involved in accident investigation until solid evidence of a crime is uncovered.
The Santa Fe Sheriff's office is really pretty good at doing what they are supposed to do, which is getting criminals and especially violent criminals off the street. The great majority of such crime is drug-related, and solved through informants. Similarly, the bulk of their effort is devoted not to the unravelling of a puzzle as on on TV, but to building a case that will stand up in court. Very little of this expertise is applicable to a complex, multifactor casualty (a term I prefer to "accident" because it does not carry the connotation of something that "just happened.")
If you look at the docket for any NTSB investigation, you'll see the difference. First a timeline is established and then the event is divided up into possible contributing factors. In the case of an aircraft casualty these would be things like weather, engines, airframe, crew, and so forth. In the case of the Rust shooting the obvious division would be weapon, supervision, ammunition control, etc.
Once the division is made a panel of experts for each area is formed and they go off and dig into the evidence. Each panel produces a report which goes in the docket and which are what you should read if you are really interested in what happened. There is then a meeting where the individual panel reports are reconciled and a probable cause and recommendations are hammered out.
The relevant agency in the Rust case should have been NM OSHB, and the loss of a life should have resulted in updated regulations for handling of firearms on a movie set. That outcome would require the New Mexico government to simultaneously engage the firearms lobby, the movie industry lobby, and the antiregulation lobby. Not surprising that they chose not to do so.