Thinking about getting back into Deathnote-Want questions answered beforehand

[Douglas]

More simply I wonder why doesn't Light make his powers known explicitly as supernatural. Nothing throws off police like downright paranoia and fear of the Unknown.

Id have criminals announce Im a Ghost of the Unjustly killed and Im here to make the world right and to not stand in my way.
And do it in a bunch of ways that would demonstrate my supernatural capabilities.

After that "Clue" finding would continue but on a much lower scale. When in a sense people "Know" the limits of my capabilities but don't know their origin, they are left downroght hopeless.

Doesn't matter what clues I gather if I am a formless spirit of death. Maybe Il have inconcistencies, but people can find divine perpose in the smallest of things and with that deflection Im left mostly unmolested.

Something along those lines actually does happen. The group investigating him figure out that however he's doing the killing, it's not with any known or even speculated mundane means. Police quit the investigation out of fear of being killed. Light openly announces (through an intermediary and using an alias) that he's working to make the world better, and that he will kill anyone who tries to oppose him. He proves the authenticity of the announcement by announcing an obvious death note kill immediately before it happens.

And, eventually, a lot of people start siding with Light (under the alias Kira) - he is, after all, successfully reducing crime rates to all time lows - and many organizations stop attempting to investigate him. That takes time, however.

Ultimately it comes down to the primary antagonist, a specific individual and his closest coworkers, being very very persistent and very very anonymous. It is the struggle between Light and L, specifically, that forms the backbone of the plot's conflict.