I think what I miss from Gene Roddenberry was the "futurist" aspect he contributed to Star Trek. Gene didn't appear to be a very good writer and came up with some kooky stories, but he did have some really cool futurist ideas that made into it Trek. Some ideas were too futurist for 20th century/early 21st century audiences, but plenty others made it into TOS and TNG and I'm all the grateful for it. I also liked how he tried to distance away from the TOS style and TOS aliens when doing TNG, again Gene wasn't a total loon, I think he was a pretty good TV pitchman and futurist, just not a very good writer/storyteller. But as others have repeatedly said, there really is no such thing as "Gene's vision" for Trek, other then something to energize the fanbase in the 1970s and early 80s.
Which cool futurist ideas were those?