I mean, don't get me wrong, what you describe as the good in Trek is something I also appreciate. The trouble is that, TOS aside, I don't see it where you do.
The reason I called out TNG S1 earlier was because it lacked absolutely nothing in terms of space-opera absurdity by comparison with Discovery, and so it's odd to me that you should abhor the one and disregard the other. But I'd also mention it in this connection because the Roddenberry-driven performances of its characters don't read as "members of a healthy family", as you describe, but rather mostly as just flat and lifeless in affect. The interpersonal stuff just reads off, like a stage play put on by disinterested actors not directed very well. As we see later in the same series, that's certainly not the fault of any lack on the part of the main cast, whose relationships become more believable, rather than less, as the show goes on. The major change is the one you cite: Roddenberry no longer exercising creative control. I think it's reasonable to consider that that change lay behind the improvement of character and relationship portrayals that I describe - especially considering that, as you also note, many of the people who made the show have said exactly the same.
Consider, too, that while the idea for TOS was his and a lot of the development was as well, he did not exercise anything like the same degree of absolute authority over that show as he did over S1 of TNG. I agree with you that TOS's characters were lively and that their friendships were obviously close, deep, and warm, and I think it's interesting that they were so in an environment much more similar to TNG's later seasons than to its early ones.
(As a side note, if you haven't read Diane Duane's The Wounded Sky, from the Pocket Books TOS novel series, I can strongly recommend it. Of all the portrayals I've seen of the relationships among the TOS main characters, in and out of canon, this is the only one I find myself always coming back to specifically for the sake of that portrayal. I'm told that "Where No Man has Gone Before" from TNG S1 was meant to be an adaptation, but God alone knows how; they're nothing alike, especially in that that episode's characters are exceptionally flat even in comparison with the standard set by that season.)
With regard to your comments on the supposed superficiality of Discovery, I feel it necessary to note that this is a judgment you've formed, and which you apparently hold quite firmly, on the basis of about four minutes of what I gather to be trailers and promos, and not on the basis of any true engagement, however adversarial, with the show itself. I find it difficult to understand how any judgment so formed could be anything other than superficial in its own right, considering that you have by your own account barely scratched the surface. It may be worth considering whether a more sustained investigation is worth your while. If nothing else, it can only enable you to better substantiate your arguments for why the show is bad!
And, sure, I wouldn't let my kids watch Game of Thrones, either, if I had any. But that doesn't make it a bad show. To be sure, there's a vast sufficiency of traits which do make it a bad show! But it being inappropriate for children is not among them.