That is why TNG failed in at the big-screen, plain and simple. The larger audience can't relate to it.
I don't think this is true at all. TNG failed on the big screen because the studio refused to play to its strengths: the characters were suited for cerebral high-concept storylines and they tried to make slam-bang action movies with them. (Note that the most successful of the TNG movies made actual use of the characters' backstories... and even that one did it clumsily.)
What seems to sell... darker stories involving flawed heroes working against a damaged/broken establishment and not quite succeeding all the way.
You're basically describing DS9.
But yes, it's completely true that the milieu that birthed the original Star Trek just no longer exists. Trek can no longer be about the happy and morally uncomplicated adventures of the American Navy in space, and I wouldn't want it to be. The core aspect that originally distinguished Trek, however, is not
obsolete: Trek can and should aspire to telling believable human stories. I don't care which century it's set in -- in point of fact I'd be game for a real
all-in reboot which actually resets the whole setting and starts from scratch -- as long as it delivers that.