I think that problem with that TNG did with Data is they were originally trying to create a counter example of Spock. Spock suppressed his humanity in TOS; they wanted to have their outsider character to aspire to humanity.
To some extent, that's true. Data was essentially a composite of Xon from
Phase II and Questor from
The Questor Tapes. And Xon was created to be Spock's replacement and thus was designed to contrast with him, to be a logical full Vulcan who was trying to explore his emotional side more so as to connect better with his human crewmates. Questor, meanwhile, was an android who was designed to mimic a human perfectly, but whose social and emotional programming was damaged and incomplete and thus needed to learn to relate to humans better through experience. I suppose Questor owed something to Spock, but TQT was also basically Roddenberry's third try at the
Assignment: Earth premise, this time replacing stoic, unearthly superhuman Gary Seven with a stoic, unearthly android.
But I think that, despite that, the developers of TNG were trying to avoid seeming too derivative of TOS. That's why Data wasn't the first officer or science officer, but the operations manager (although he ended up playing the de facto science-officer role anyway). And it's why the first couple of seasons didn't define Data's personal journey as being about emotion specifically, just about pursuing his humanity. I just did a search of the online transcripts, and Data hardly ever uses the word "emotion" in the first two seasons, and often does speak of feeling things (like how empty he will feel after Tasha Yar's death), or doesn't correct others when they describe him as feeling things. The first suggestion that he didn't feel emotion (at least not the human kind) was in "The Schizoid Man" in season 2, and there was a line in "Peak Performance" that reinforced it, but in neither case was Data himself the one saying it. And it didn't start to become a defining aspect of Data's characterization until "The Ensigns of Command" and after.
The problem is the idea that he was a counter weight to Spock got forgotten pretty much and later shows used Data as the template (i.e. the Outsider who wants to be more human) without that context.
Did they? DS9's outsider character was Odo, and he specifically didn't
want to be more like humanoids. He tended to look with scorn on humanoid behavior and he was more interested in discovering his own people's origins and nature. The Doctor on
Voyager was sort of a mix of both -- becoming more "human" as he explored his potential, but also embracing his nature as a hologram and how it gave him different, often greater potentials than a human. Seven of Nine resisted rediscovering her humanity, and though she eventually did accept her human side, she never entirely let go of her Borg side. T'Pol came closest to the Spock template, a full Vulcan with a condescending attitude toward humans, but with difficulties controlling her emotions due to one factor or another (the writers couldn't settle on just one).
The only one of those characters that comes close to using Data as a template is the Doctor, but he's more true to the original, Questor-like conception of Data, an AI capable of emotion and merely lacking social skills due to inexperience. But he also had the condescension of Spock and Odo.
To be honest, a character like Spock that puts humans in their place every once in a while is sorely missed in modern Trek.
You mean a character like Odo, or Quark, or Garak, or the Doctor, or Seven, or T'Pol. Or even Phlox on occasion (e.g. pointing out that Denobulans handled genetic engineering far better than humans did, or being amused and dismissive about human sexual hangups).