TNG didn't really take off until after Gene died, if you notice that's when we started to get more character based episodes, rather than the plots being focused on solving the problem of the day.
Several of the actors had mentioned that they had approached gene about expanding their characters but he was pretty set on having the "problem of the day" format.
I believe this happened around season three which would have been around the time Gene passed. That's really when the series took off and the characters became more relatable and endearing to viewers, where Picard became less rigid, Riker became less awkward, and actually earned more respect after his handling of Wolf 359 etc...
Data became more, well, human...Worf showed other emotions and became a vehicle for comedy, Geordi became the nerd/geek that was so beloved and endearing...Counselor Cleavage (Troi) got less melodramatic, Crusher got to explore ethics and principle far more...
So yeah seasons one and two, when going back, you definitely see a paradigm shift from season three onwards.
Even in season 2 there were positive format changes, with season 3 just polishing up what was left. The character drama stuff also increased, though there felt more like a balance. Later seasons would get too character-focus as well as soapbox preachy. Season 5 definitely started that trend, which also had the highest ratings, but that just meant a lot of people loved it at the time. Cue Fad Gadget's song "Swallow It", but when you have highly-rated garbage episodes like "Disaster" getting so many character traits wrong or forgotten solely for the sake of teh drama, combined with skipping out on basic science 101
that the super-ishy cooties-laden season 1 there somehow got right time and time again, despite some faltering plotlines... Even some friends and family at the time that they preferred the older seasons in reruns because they actually had adventure and action stuff. A quick tangent about science accuracy: Suspension of disbelief is inevitable no matter what the show is (even "reality shows"), but that only goes so far. We know the ship and FTL travel and teleportation and replicators are fantasy. Other elements within this framework clearly make up for it and keep us invested or else we'd have balked from day zero zero one. It's why one can be a fan of "Space 1999" where, beyond the outer level premise that we know is impossible, everything despite that holds up and compensates.
Gene also died during early season 5. The Lwaxana/Alexander episode is just about 4th wall when you think into it too much.
Data becoming human... well, originally he was more like a Pinocchio trope and not just a robot... depending on episode... The ones where he feels he's trying to emulate humanity and failing, instead of engaging in the following BASIC program, are so much truer to the idea of Data (and... Lore...):
10 PRINT "I am an android"
20 GOTO 10
RUN
Worf: He also used to be the overused punching bag trope because, if Worf gets the snot beaten out of him, what chance do the softer spongy humans have apart from "zilch"? That said, "Datalore" is a **** episode on paper but, damn, individual set-piece scenes more than make up for it. The bit where Worf is pummelled to show off how butch Lore is is jaw-droppingly creepy, for the right reasons, every single time. But who wants to rewatch the same scene by hitting the rewind button then play every 20 seconds and not everyone had VCRs, so the trope remained in use where he'd continue to get pummeled in umpteen episodes, but I digress.
What's wrong with Geordi, who was always a bit of a nerd and even in season 1 he was ending up in Engineering more often...?
Crusher was used too often a popsicle stick cipher for inane dialogue, especially for the overly-preachy "Ethics". Be glad she wasn't in the episode "The Hunted" where Worf got her lines, which seems odd as he usually spouts "it is a good day to die" and other depressing one-liners that I'm sure the DSM-V revised edition has an answer for and all that. I think Data may have gotten some Crusherific lines too...
The best of both worlds between character and plot and structure were definitely seasons 3 and 4, though some inkling could be felt in some season 2 episodes.
S1 and S2 are my favorites in terms of storytelling - I find them the most enjoyable to watch. I love the 'standalone episode' format, which made each episode unique and memorable for me. Recently, I noticed that while compiling a list of episodes to watch with my father, I included almost every episode from S1 and S2, but fewer from later seasons. While later seasons produced strong character-driven episodes like Data's Day or Ethics , many others lacked the depth and impact of the first two seasons.
To answer the topic's question - I agree, but I think this is partly because of the shared loss that unites the family, which would have created a completely different tone for the series.
The later seasons had more viewers but they did indeed lack the depth and oversimplified way too much. With a few exceptions, even "The Masterpiece Society" - a cynical redo of "Pen Pals" in ways, has one or two of the best Geordi scenes ever, which also remembered that his VISOR has traits he uses on a regular basis. Except for "Disaster", a real piece of Star Drek but I digress...
S3 and S4 for me, but I love S1 and S2 way more than S5-7 for the most part as they do feel more like exploration of the cosmos and civilizations, with less inane navel-gazing that even eschewed the basic science that the earlier seasons strived to get right. There's that "Ethics" episode reference again, as well as "Disaster", among others... "Data's Day" contrived a little to get Data not to Cindybradytattle to the Captain the atypical events he was witness to with being asked for the codes (Data is literal, but THAT literal? The golden rule is always chain of command and to let the commander know anything that differs, what with "A Matter of Honor" confirming that precedent and all, if not earlier), but keep watching and the payoff at the end makes up for it and then some.
Picard wouldn't be happy on a planet of luddites like that, he needs to constantly explore or at least learn.
Also DS9/VOY got a fraction of TNG's ratings so involving them in a film was just a non starter. It's why Paramount didn't want INS to be a Dominion War movie, the bulk of the TNG movie audience wasn't watching DS9 and would have no idea what was going on.
Correlation not being causation prevailing, VOY quickly becoming TNG-Lite despite its original premise of factions forced to work together feels like whiplash thanks to DS9 losing viewers due to its serialized style...
A lot of the TOS tropes don't work as well, with TNG and its contemporaries' greater continuity. For instance, inorganic life in "Home Soil", which between holograms and androids, becomes common as dirt in later shows.
True for multiple reasons and TNG was right to be influenced by TOS stories rather than just redoing them*, but even TOS had androids all over the place. And more often than not came from Andromeda with or without their makers. I still love "Home Soil" for being the most sci-fi episode TNG could be... the only difference is, the glowing crystal thing felt like a naturally occurring creature whereas androids and holograms were obviously programmed constructs. The EMH stories involving rights were just a derivative of Data's and at least Data's felt more organic in exploration. If not way too repetitive since "offspring" and "quality of life" just reek "measure of a man" all over again and I would never want to compare those to TOS...
* "The Naked Now" = lame redo
* Inner Light = their innovation to re-mold elements "The Paradise Syndrome" but in a new way that doesn't feel like an overt copy
etc