VOY's premise DID constrain them too much. Then when they figured "Okay, let's try something interesting even if it means breaking the premise" and DID that the reaction was always negative.
Again:
There's nothing in there about not being allowed to do anything interesting or important. I have no idea where you get this idea, aside from the fact that Janeway didn't have a pre-built backstory about being a famous captain or a Holy Icon.The premise was simply that they're in a completely unexplored zone and cut off from Starfleet.
Then how come, in all those examples I brought up, the reactions were negative?