TNG was really a product of it's time.
Would this type of show resonate with the modern audience at all?
I agree that it was a product of its time--absolutely. That may be another reason why the movies, with their increasingly darker themes, were not as well received as the series. In addition, the novels post-Nemesis have also been "darker," which has led to a varied response. I think a TNG relaunch would inevitably have to reflect its time, and there are many elements that may not resonate as well with today's audience.