I don't know if Roddenberry himself was a good influence on TNG after getting it started, the series got way better once Michael Piller took over. But the idea of staying true to 'Gene's vision of Star Trek' (ie. the vision of the future created by the TOS team of Roddenberry, Gene Coon, Dorothy Fontana etc.) has benefitted the franchise a lot. Writers found Roddenberry's rules about not having interpersonal conflict and so on frustrating, but they made TNG into what it was, something that was different to anything else on TV. On DS9 Ira Behr pushed against Berman's determination to stay true to Roddenberry's vision, and I think having to be creative within those limitations is a big part of why that series is so good.
So I think Star Trek is generally better with the ideas, restrictions, optimism and humanist philosophy attributed to Roddenberry, and when it strays too far from them it loses some of its identity.
So I think Star Trek is generally better with the ideas, restrictions, optimism and humanist philosophy attributed to Roddenberry, and when it strays too far from them it loses some of its identity.