You are not seriously comparing Kirk and co. to Abraham Lincoln?
Bringing life again to a real historical figure through the medium film is something else entirely from telling stories about fictional characters.
No, it's an apt comparison. Lincoln's life is documented (largely) although there will always be questions because not every moment of his life is documented. Events in his life can be (and are) dramatized with a measure of creative leeway to make his story and the events compelling. We know the outcome, but we can still chart the events in a compelling way.
In Star Trek
it's all fiction. All that is set in stone is what has happened to the characters in TOS' three seasons in so much as they're approaching this as if they are indeed doing the unseen fourth season. They are not constrained by having to acknowledge what was seen in TMP or in any film or series afterward.
Yet even if they do acknowledge the events of TMP and a nod towards TNG they can still do a great many things as long as it's not inconsistent with where they end up in TMP (and as long as it's rationalized in a credible way).
Any of the characters could get married or promoted or whatever as long as they're back the way we see them by the time of TMP.
Or put it another way. Kirk was the hero of the series. It wasn't going to happen that they would kill him off or any of the other series regulars for that matter. That certainly didn't preclude them from telling compelling stories.
Therefore I reiterate that the only creative limitations are self imposed ones rather than in fact.
I sense that what's really being asked here is whether one could apply a Game Of Thrones
style of storytelling to TOS. In that regard I would say "no" because that would definitely be straying too far from the kind of storytelling done on TOS and all other television of that era. If the STC producers are limiting themselves in that way then I think they're right in doing so.
Sorry, but telling compelling stories that inevitably have to end up where we know they will end up in a style that hasn't been relevant in a very long time is by definition NOT creative freedom.
There can never be any surprising, unexpected changes or lasting consequences for the characters we really care about.
That's why these fan production have to bring in other characters (Peter Kirk and McKenna, for example) to have at least some wriggle-room.
I wish the fan productions would, like Abrams, put their own stamp on Star Trek. Phase II and, now, Continues have shown that they have talent, and I'm sure they could pull off their own interpretation rather than simply recreating (though they do it with loving devotion and I admire them for their efforts).
No, the only limitation is the one you perceive in your own mind. You are predisposed to see it that way so you accept it as a fact when it isn't any such thing. And if you want a reinterpretation of the TOS characters and setting then you have JJ Abrams, and therefore I don't see what your beef is.
The fan productions are interested (mostly) in continuing the series that was aborted. They're trying to give fans what they would have liked to have seen. If it isn't what you want to see then there is nothing to be done about it.