Someone else very well may have made a Forbidden Planet inspired sci fi voyaging show. CBS had Voyage to the Bottom of the Sea, it was already using monsters from Lost in Space on alternate weeks, if they'd put it in orbit, there's star trek. It would not have been called Star Trek is all. It would also have looked cheaper, but again that has nothing to do with Roddenberry. Lucille Ball wanted to be sure her flagship programs, Mission Impossible and Star Trek looked top notch, and she made certain that had good budgets. She was not amused with Gene wasting budget on giving his mistresses jobs. More than likely this other show that almost certainly would have happened it would have a lot of the same writers and maybe even some of the same actors and actresses, maybe even some of the same set designers and prop guys. It was a small world in Hollywood.
I'm not saying Gene Roddenberry did not have a really good idea for a TV show, clearly he did. It was not his work alone though, and as others have stated there came several points where he nearly killed the franchise. Those too are facts. Gene Roddenberry was losing and chasing off writers left and right in the early days of TNG and many of those episodes show just how badly the show needed a change in leadership. None of the movies beyond TMP would have been made if Gene had had his "vision." He wanted that Kennedy assassination movie. Studio execs passed on it every single time.
People have to be distanced from their own creation at times. In another industry years back, the U.S. government was seriously considering taking action to make certain Henry Ford didn't take BACK control of Ford Motor Company during WWII for similar reasons: his vision, whatever it had been, no longer worked with the needs of the age. Discovery gives Roddenberry credit in the opening credits, that coupled with whatever cut his descendants get, should be enough. It doesn't need HIM.