Warner Bros. is probably more paranoid and thinking in terms of financial success in regards to Superman, but I think there is still a grain of truth to what they say. People still love Superman for idealism, especially kids, but I think there is a degree of naivety and privilege that exists in Superman stories (or at least the archetype) that make them feel dated. The idealism and earnestness is what can be timeless, but the nobel, white country farmboy being a symbol of my idealism? It rings a bit hollow to me, especially since people say he represents an immigrant story, but I don't feel it reflects that in a modern context; white-passing, raised by American, English-speaking parents. That's just my opinion though for why I loved Superman as a kid but don't care for him as I grew older, even though I still became a big fan of Captain America in the MCU for his idealism.
I think that is why there is the desire to make Superman cynical, because they don't know how to square the idealism of a country boy without coming across as naive. They don't know how to have him be goodhearted without coming across as a goody-two shoes who is basically a cop that follows all the rules, not just having a strong moral compass. They want to make him feel more worldly and give him an edge, and in the case with Snyder's Superman, it's easy to see how that impulse can go so wrong and it can be so misguided. I mean, if you think about it, Superman is supposed to be a symbol for masculinity and that is why you get takes like Snyder's about what it means to be a man, while others such as myself see a potential for a more modern, less toxic interpretation for masculinity.
I'm not a fan of comic Superman, but I assume it's something that writers have had to already think about for decades, and maybe they have found a solution, but it hasn't quite made it to the movies. I do think that the Captain America films have worked pretty well because they put an idealistic person against a world that was morally grey and challenging his world view. Even the way Spider-Man has often been portrayed, his biggest challenges in his personal life are testing him for what he believes in and pitting the things he wants against what he believes is right. Where I think that Captain America succeeds that Superman often hasn't, is that Steve starting as this skinny kid that can't even pass a physical to be enlisted in the army is like a quintessential underdog. When he sticks up for the little guy, you believe it because he was the little guy. Spider-Man is the same way since he was the nerd that got bullied before he got his powers. Superman on the other hand has always been exceptional, he was born special. He was like a rich kid that had access to the best schools and he may be a good person, but he also hasn't had to struggle, so his confidence can have an air of smugness and his altruism can have a hint of charity and pity for the less fortunate. You can't believe for a second that Superman thinks he's above others or the whole character crumbles, or at least if he has those human impulses, you have to acknowledge it as a flaw and out of character. He has to have a believable gentleness, kindness, and humility, and it might not hurt to show that it takes work to be a good person, and that for how effortless every other task is for someone like him, the hardest thing to do can be trying to make the right decision.
If you want to make a modern and believable Superman, acknowledge that for a character that is analogous for America being a world super power, one which makes the Homelander-type evil Superman comparisons/deconstructions all to easy to make, you need show that he has the power to do incredible things, but might does not make right. He may not be as burdened as Peter Parker by great power and great responsibility, but he should at least feel the weight of it since he's in a unique position, and it shouldn't be a Snyder-esque sulking about his burden to help others and a dilemma about whether he should help someone else or do something for himself, it should be that despite his morality and his ability, things aren't always that simple. At least, that is my take. That is one issue I had with Steve Rogers in the MCU, because even though they show hint of his flaws and his humanity, Steve is mostly always right, even when he's wrong. What more endearing way to portray a person with a strong moral compass than for them to admit when they are wrong and to struggle with what the right decision is instead of having scenarios almost conveniently slot into a more binary outlook of there being clear right and wrong.