Cynicism like this does make it hard to believe...
I think that's a bit insulting, to be honest.
"Cynicism" is not at all the issue or driver here. Every good inspirational story in the history of storytelling is about a protagonist or a group or characters overcoming adversity to achieve a greater goal.
I fully believe that humanity can get better, and unlike many, I fully believe we have made amazing strides in our history already that prove that we have this capability. But those strides are drenched in the blood, sweat and tears of sacrifice, colossal change, cultural and societal uphevals, etc. We don't get better because it's the right thing to do. That would be wonderful....but people and societies don't work that way.
On both the personal level and the broad society level, change happens due to challenge and struggle.
As a viewer, I don't care at all to have a wonderful, perfect, harmonious future handed to me on a silver platter. I'm more interested in the struggles that humanity had to (and has to-
present tense) go through to achieve those things...and to maintain those things. I'm more interested in real human beings who still have all the same inherent weaknesses and failings that are hard-wired into us and watching them achieve / overcome IN SPITE of those shortcomings. I have no interest in seeing the shortcomings eliminated via humanity's "evolved sensibilites" that happened somewhere off camera. "Yay, look at everything we can become" is about where it ends if we want storytelling in that mode. Sorry, not my jam.
To me, having the virtuous and noble people living in the perfectly utopian society is not inspirational at all. It's dull, unrealistic, unimaginative, and yes.....child-like in its simplicity. It's one of the reasons TOS, DS9 and DSC appeal to me far more than TNG and VOY. The magic and the inspirational value exists in watching real, relatable people and societies battle to better themselves. Sometimes even failing (oh the horror...I know....but it happens from time to time). But ultimately picking themselves back up and doing the right thing even in the face of all those challenges and barriers.
And, frankly, that's the "positive future" I've always appreciated in the versions of Trek that resonate strongly with me. Kirk's "We're not going to kill....today" is, for me, far more important, realistic and impactful than Picard droning on about how money and hunger and prejudice don't exist any longer because we have some replicators, an FTL drive and an "evolved sensibility." It's shallow and unimpactful.
YMMV