The simplicity of The X-Files format has to be its greatest strength. The FBI investigative procedural gives a credibility to the story world that adds a sense of realism to the paranormal stories. Other strengths include the dual-protagonist dynamic between skeptic and believer in their search for the truth, the element of surprise built into each episode, and the string of intriguing, sometimes enigmatic characters we encounter throughout the series.
I would find it difficult to discard any of these elements as they are so central to the success of the storytelling. The change might be less in terms of components and more in terms of refreshing the narrative structure of the series to suit today’s tv viewing habits. It might be possible to balance the ‘monster-of-the-week’ with an extended seasonal narrative.
In terms of what audiences would be looking for in an X-Files reboot, I think they would be looking for the same thrilling encounters with paranormal phenomena, character-focused storylines, and probably a nostalgic nod to the original series while being relevant to today’s world.