If jazz was a part of DT in the first 8 albums... that didn't die, if you're going by that standard. IT has multiple jazz-inspired moments like that swung main riff with a lot of bluesy flourishes or that crazy piano cycle that happens just after the vocal part in The Pursuit of Truth. Hell, the trade-offs might be condensed, but they're still there and a fairly regular part of the band's sound. If we're going to call Take the Time jazz influenced, I'm not sure why it wouldn't also apply to S2N, A Life Left Behind or Surrender to Reason (plus The Alien, but I'll give the benefit of the doubt in that regard).
I find the idea of the first chord of Dystopian Overture defining songs as far reaching as Chosen, The X Aspect, Moment of Betrayal, Hymn of a Thousand Voices, The Gift of Music and Ravenskill... a bit reductionist, to say the least. It's likely the most eclectic album of their discography with relatively few contenders. Just because a common thread is a few louder textures in the form of distorted guitar chords, it doesn't discount that.
Also... I love Octavarium too, but I don't know about it being a classic DT album. I know this argument is probably pretty well worn out by now, but when you've got two songs that are almost plagiarised from others (These Walls being startlingly close to Linkin Park's From the Inside and Never Enough being a DTised Stockholm Syndrome by Muse) and more that are nevertheless startlingly similar to the styles of other bands, it begins to feel more like a 'best of early 00s, done by DT, plus a few new songs' album than a classic DT album. Not to mention, The Answer Lies Within feels like a pretty par-for-the-course alt-rock ballad that does little to distinguish itself even for what it is, nevermind how it's imo already eerily similar to Anna Lee stylistically (itself also seemingly cut from the same cloth as contemporary radio-ready stuff without really making it their own, though I do like both songs still).
I can give them props for trying these different things, but it's another question as to whether I think it made those songs uniquely theirs. I think there's a difference between imitation and integration. Scenes might have moments like Home with sections that feel suspiciously similar to other bands (Tool in that case), but it's usually limited to a riff or two and they tend to morph the entire package something more distinct. That's not to say there aren't still moments like the former with stuff like Build Me Up, Break Me Down, The Looking Glass and Paralyzed, but it feels like the exception more than the rule. If I was to recommend a definitive album to someone unfamiliar with the band, Octavarium would be near last in my list of considerations for that reason.
Also agreed with the point before that IT's classical orchestra was something unheard of in studio DT. Yes, it was part of a wider epic... but it's not exactly a fleeting moment either, not to mention that the melodic character of the song takes on a symphonic angle that wasn't necessarily done before in that kind of reflective, maybe Romantic-era style with the Tchaikovsky vibes, distinct from how Six Degrees did it (even disregarding the orchestra being all MIDI there). I'd also say that Pale Blue Dot's own harmonic style is pretty unique too, with that kind of tense, spacey dissonance being a feature even throughout the vocal parts.
As for the popularity of Scenes vs Train of Thought, you could probably do with using more modern metrics. Scenes has a significant leg-up on Train of Thought as each have weathered the test of time, I think it's fair to say. I'll also add that to say Train of Thought added something to the DT sound is something of a stretch. Between The Mirror, Lie, Caught in a Web, The Glass Prison, Blind Faith Home, Burning My Soul etc. I'd say the precedent was pretty clearly set out. It just put the spotlight on the metallic elements that were already there. Hell, even the rap thing they'd already done on Just Let Me Breathe. If someone was to say that DT stopped stretching out their sound since Six Degrees and that their classic era ended with that, I'd say that's a fairer and more consistent assessment but I'd still disagree with it on the basis of The Astonishing introducing a decent amount of new (much of it at the very least uncommon) sounds to the table.