Dunno if you remember the '80s, but I do. If anything, the whole concept was even
less socially acceptable then. "Single mothers" and "deadbeat dads" were both ostracized figures in the popular imagination; these days, at least the former are usually viewed with a modicum of respect.
Regardless, I don't think anything in this scenario would've involved Kirk having to "prove fatherhood." We have no indication that Carol would have lied about it if asked. What's at issue was not his status as biological father, but what to
do about it.
On average. Ceteris paribus. Studies like that inevitably rely on a whole lot of variables and contingencies. Some of those are under the control of the people involved, and some aren't (like the economic world we live in, for instance). What's best for a hypothetical typical person (or family) isn't necessarily best for any specific
actual one. It's not statistically valid to generalize from the former to the latter; that's the
ecological fallacy. Besides, in this case, "if possible" wouldn't appear to have applied, at least not without generating conflict that would be a counterweight against any potential benefits.
It seems reasonable to infer that Federation courts, just like today's, might well have imposed mandatory visitation
if either parent had insisted. But courts don't do such things of their own volition, and in this case Carol obviously wanted the exact opposite, and Kirk deferred to her wishes.
So, in other words, lots of different emotional reactions are possible depending on the details of the specific situation, and we can't draw any valid inferences about how David actually felt about things.
Because he can't force his way into it without causing conflict with the mother. Why are people deliberately overlooking this?
It presumably would not have been, had Kirk chosen to take the issue to court. In those circumstances, the court would have been tasked to determine what kind of parental custody or visitation arrangement would have been in the best interest of the child,
given the pre-existing conflict between the parents that brought the case to the court. However, Kirk had it within his ability to avert that conflict in the first place by deferring to Carol's wishes about how David should be raised, and it was entirely reasonable of him to do so.
After all, he was honest enough to recognize (as she did) that the only way he could be a
regular presence in David's life would be to completely upend his career and abandon Starfleet, something that neither one of them actually wanted him to do. Short of that he could at best be an absentee parent, with visits and communications no more than sporadic, and little actual involvement or influence in David's life.
Kirk might well have preferred to have at least that — after all, remember that his question to Carol that prompted this whole discussion was "why didn't you tell him?" — but she apparently nixed that as well. We don't know what if anything she actually did tell David about his parentage; all we know is what she
didn't tell him, namely that his father was James Kirk, the famous starship captain.
Yes, it was. She was dreamed up in conversation between D.C. Fontana and DeForest Kelley himself, and she was included in the show's Writer's Bible, and if that's not precisely canon it's close enough for me... but even more on point, if you want an on-screen reference, McCoy specifically mentions her in dialogue in TAS "The Survivor."
Yes, that's the consensus interpretation of things: McCoy and his wife split while their daughter was a child, but he remained in touch, and she was college-aged during the FYM. The obvious difference there is that, whatever the circumstances of McCoy's divorce, his wife didn't make a point of wanting him to stay away, as Carol did with Jim.
Kudos on your sense of responsibility, I suppose (and I'd find that a somewhat less discomfiting word than "obligation" in this context). However, your final sentence somewhat undermines that. "
Of course I can improve his life: I'M HIS DAD!!!" is an entirely egoistic claim, one that's more about your own sense of identity than the child's actual well-being, and certainly isn't a claim anyone should accept at face value. Almost anyone can
become a parent, after all, but that doesn't mean anyone is necessary capable of
being a
good parent. Ask any teacher, or psychologist, or social worker, or family law attorney, or pretty much any other kind of relevant expert... the decided majority of actual real-world parents are
not particularly good at it, and some are downright awful.
We can surmise that Kirk might have preferred such an arrangement, as I said. But a court fight is what it would have taken. How does anyone not see that? What makes Carol's remarks on the topic seem anything less than determined and decisive?
Well, if that's your perspective, then you appear to be saying that Carol was selfish. Perhaps so, although I think her perspective was also reasonable. Given the attitude that Carol and her professional colleagues had about Starfleet — she was cautious about it but at least willing to give it credit for having "kept the peace for a hundred years" (oops, another contradiction courtesy of DSC!... but I digress...), but others around her were even less generous — it's understandable why she might have preferred to avoid having her son feel torn between those two worlds. Lots of people here keep mentioning present-day examples of kids with one parent in the military, for instance — but if you take such an analogy and further posit that the custodial parent has a strong
dislike for the military, and lives and works in a community that shares that sensibility, how would visitation from a parent who's a high-ranking officer make life any better or easier?
At any rate, whatever one concludes about her motivations, it still doesn't reflect badly on Kirk. There is simply no plausible scenario in which he could've been a part of David's life without introducing additional conflict and stress for all three people involved.