I've read
Harlan Ellison's work on his dealings with Star Trek creator Gene Roddenberry during the writing and taping of the classic episode
City On The Edge Of Forever.
While Ellison's original screenplay (in which Kirk attempts to save Keeler, and is stopped by Spock) is excellent tragedy, there's no doubt that it would have drastically changed the character of Kirk as envisioned by Roddenberry, and would have made for a very different series.
So...with a divergence point in which the budgetary concerns of Ellison's screenplay are addressed to everyone's mutual satisfaction, and the original ending stands, let's have other famous science fiction writers drawn into the orbit of the show. Let's say that Heinlein needs the money, that Asimov, Bradbury, et al are attracted for their own reasons, and that the show runs indefinitely as a result of the attraction of the talent.
What changes would we see in the characters, or in the theme of the series? What stories would come about as a result?
For an extra challenge, let's say that any story pitched in this thread must conform more or less to the continuity established in previous posts. For instance, if Heinlein writes a story in which the Federation is established as a purely capitalistic society, then we can't have a story in which they're shown as purely capitalist or communist...at least not without a decent rationalization.
Example from the paragraph above: In the first season, Robert Heinlein submits a story largely inspired by his previous works, in which a human Lieutenant on the Enterprise is discovered to be hundreds of years old. The Federation wants to reassign the Lieutenant to Earth so that they can research his longevity in a controlled environment. The Lieutenant himself has no desire to be used as a lab rat, and plans an escape from the Enterprise. In the exciting climax, Spock and McCoy help the Lieutenant escape (Spock sees the logic, McCoy thinks it's simply the moral thing to do) despite Kirk's reluctant following of the order given. The Lieutenant escapes to a frontier planet. Kirk, Spock, and McCoy are viewed with some suspicion by their superiors, but nothing can be proven.
Establishes: Kirk as torn between duty and right action, Spock and McCoy as willing to buck orders for a moral/logical truth, the existence of frontier planets outside Federation/Starfleet jurisdiction.