What is it with Star Trek repeatedly hammering home that under different circumstances, either a Reman slave upbringing in Nemesis where he rose to (briefly) rule the Romulan Empire or in the Confederation timeline in Picard season 2 where he was a man of great wealth, Jean-Luc Picard is a monster capable of unimaginable evils? Mass murder, rape, full-on genocide. It's like we're in the one universe where he's a nice guy.
It's the same idea of wondering about really nice people. There is an expectation, almost a distrust, of people who are nice, expecting an ulterior motive, or a dark side that they don't tell people. It's a weird concept for people to see only the good. There's always an expectation of a dark side that would be let out in the right circumstances.
Because polar opposites work best to hammer things home. And Trek loves its "this dark timeline has everone being evil" trope to show and boast about the fact that its prime timeline is "the good one". And with a character like JLP, you have the chance to REALLY hammer it home because he's such a good guy usually. (He's far from perfect, he has a lot of flaws, but he's generally a good guy. And I don't say this sort of thing lightly usually.) Although I'd prefer a bit more nuance as a whole, too. In a bad universe I think he'd be more the sneaky, silently deadly type with elaborate schemes and plans to achieve whatever his current objective is. He's the sneaky type already in the good universe (people constantly seem to underestimate him because he looks smol and cute and harmless... big mistake), he just usually uses the ability for 'good'. And, in a different universe he'd use it for evil. Much like Sejanus in I, Claudius. (Example chosen deliberately, of course.) THAT's the "bad universe" type I think he'd be.
I mean, the point is not that Picard is "really" a bad person. The point, which I think Picard himself is aware of and would agree with, is that we are all shaped by our culture and our environment, and that a person with the potential for great good also carries the potential for great evil. Prime Picard comes from a culture in which his material needs are met and in which his culture encourages compassion and empathy, and therefore when he made the choice to really try to live up to his potential, he was encouraged to do so in ways consistent with those values.
It's the same principle as taking note of only negative events or developments. It's an evolutionary/genetic thing. Good things our brains don't have to react to or take special notice of because they won't harm us. Negative things however we have to react to in order to avoid harm, so our brain brings them to the forefront. Same with expectations for something or someone to be potentially dangerous, those expectations can save us in a life-or-death situations by preparing us for it.
I never thought about this, but it puts those YouTube recut parodies where he's an evil megalomaniac in a new light! However, remember that in "Yesterday's Enterprise," that AU Picard was still noble and heroic. And in "Tapestry" he's a 60-year-old dweeb, but still a totally nice dude. It seems that Picard just varies a lot, under different circumstances. Given how restrained, controlled and deliberate his personality is, this makes sense. Jean-Luc Picard is a man who forces himself to act appropriately based on the principals he was raises with and the behavior his job calls for. The Picard raised on utopia Earth, and working in Starfleet, very deliberately acts out the principals of both. Is it any surprise that a Picard raised by Remans would act more Reman than Reman, or that a Picard raised on a fascist Earth would be the best damn fascist on the planet? Compare to characters who wear their natural feelings, or lack of, on their sleeves. Data would likely be the same logical, socially clueless Android no matter what society he was brought up in. B'Elanna Torres would have volatile emotions and a talent for Engineering whether she's in Starfleet, the Maquis, the Mirror Universe, or a WWII French Resistance cell. But Jean-Luc Picard has tailored his mannerisms and reactions to his society. No surprise there are so many different Jean-Luc Picards in the multiverse.