For me it was the opposite.
Roddenberry's Box was not some technique to get writers to think more creatively or write stories that would add to the overall uniqueness to Star Trek. It was just a tool that Roddenberry insisted on so that his creative input would have a more tangible presence in the show.
And even when it was applied, it wasn't fool proof either. Season 3's episode "The Bonding" is a great example on how the box should never be looked at as an absolute. We have numerous crew members mourning the death of an officer and we see how each one of our characters is affected by it in different ways. Riker feels the heavy weight of loss despite not knowing this crew member very well, Worf is angered about how her death was senseless and Picard takes on the responsibility of informing the their families. But when it comes to the officer's son, the one character who should have been at the very center of this emotional turmoil, we get Roddenberry's Box in action by showcasing Jeremy to be alright with his mother's passing.
And the thing is, I LOVED the parts of the episode where the crew are affected by Aster's death. I never liked the "Red Shirt" syndrome so seeing what should be a red shirt die in an episode and having her death affect the crew not only showcases that these characters actually give a crap about what happens to everyone, but also how they deal with it.