So - when TNG began airing, I would have been about 15 - right squarely in the perfect formative timeframe - it was "ours" more so than the original series ever was.
100% agree. I watched all the originals too, and enjoyed them, but they absolutely felt like an earlier generation, building on a culture that did not match how I felt. As you say, TNG was all ours. <fist bump>