a good analysis, but a somewhat skewed statistical sample.
I mean, look at the crew in TNG and see what it suggests about the adult mortality rate:
Picard: both parents dead
Riker: one parent dead
Crusher: both parents dead
Troi: one parent dead
LaForge: one parent went missing, presumed dead
Yar: both parents dead
Worf: both parents dead
Wesley: one parent dead
Weren't Ro's parents both dead?
Many of the single child couples you noted also had one parent die or leave while the child was quite young: they may have been planning more children, but didn't get the chance. And single parents in the 24th century seem to have the same problems dating that single parents in the 21st century face: few we have seen marry again until their child is grown if at all.
I think what we have identified here is is simply this pattern: central characters tend overwhelmingly to have little or no surviving family.
I acknowledge that our sampling is
probably skewed, but the main characters are the only samples we have. I want to be more thorough this time, so please excuse some repetition on my part. My point is that in the 24th century, the characters with dead parents were not on Earth, but had either one parent serving in Starfleet, known to be hazardous, or living off Earth on a colony world where problems that don't arise on Earth are more common. And two of your points - Worf and Ro - aren't from the UFP and their situations cannot be used as sampling for a typical UFP family.
Let's begin -
22nd Century
Archer: The only child of Sally and Henry Archer, born and raised on Earth. Henry Archer's premature death from a disease may have prevented the birth of any other children. Nevertheless, the Archer family had only one child, who was raised on Earth.
Tucker: Trip had one sister, and according to Memory Alpha, a brother. So Charles Tucker, Jr. and his wife had at least three children, all raised on Earth.
Reed: Malcolm had a sister, raised on Earth.
Mayweather: The Mayweathers were a Boomer family, so they did not raise their son Travis and his two siblings on Earth.
Sato: Hoshi had two siblings, and was born and raised on Earth.
T'Pol and
Phlox aren't human, so their families would tell us nothing about 22nd Century Earth-based families.
In the 22nd century then, of the 5 human characters, only 1 was a single child, 1 had one sibling, and 3 had 2 or more siblings. But one of those multiple children families was not based on Earth. So out of 4 Earth-based families, 2 had two or more children, and 2 had two or fewer children. The Human population growth rate on Earth may have been flat or positive.
23rd Century
Kirk: Known to have one brother, George Samuel, in the prime universe. James considered himself to be "from Iowa" (he only worked in outer space), so he at least lived on Earth long enough to associate himself with Iowa. He may been raised in Iowa, but he also spent time off-planet at Tarsus IV as an adolescent.
Spock: An only child, but only half-Human and not raised on Earth.
McCoy: No known siblings, but fanon says he had a daughter, Joanna, with his ex-wife.
Scott: Scotty may have had a sibling, but I'm not clear on whether Midshipman Peter Preston was his nephew or not. The lines referring to their relationship were cut from the theatrical release of TWoK, but included in the TV broadcast. Which version of the story is canonical? At any rate, Scott may have had a sister, but no indications of other siblings, and he may actually have been an only child, born and raised on Earth.
Sulu: No known siblings, but his family life was not discussed or mentioned canonically. We know he was born in San Francisco, and had at least one daugther with an unknown spouse or significant other.
Chekov: Known to be an only child, born and raised on Earth in Russia, the source of all things cultural (according to him).
Uhura: No known siblings, but like Sulu, no discussion of her family canonically. Probably born and raised on Earth, but no canon information on that either.
In the 23rd century, we have 6.5 human characters, but 0.5 of them were not raised on Earth. Of those 6 families, 2 of them (the McCoys and the Chekovs) had only one child, 1 (the Kirks) had two children, and 3 of them (the Scotts, the Sulus and the Uhuras) are of unknown size. Again, population growth may be flat, and possibly negative in the 23rd century on Earth.
24th Century
Picard: The second son of Maurice and Yvette Picard, younger brother of Robert. Born and raised on Earth, in a two-parent home with his sibling, and apparently his parents were dead by 2364, but how long before we don't know. They may have died recently before the start of TNG, and of old age, which wouldn't be unnatural even in the 24th century. Nothing unusual about an adult having lost both parents to old age.
The second generation of Picards, Robert married to Marie, had only one child, Rene. Tragically, Rene and Robert were killed in a fire in an unknown location.
Riker: The only child of Kyle and Betty Riker. Presumbably Betty died prematurely, and so there may have been the prospects of future younger Rikers, but the fact remains that Will Riker ended up an only child. (As an aside, according to canon Kyle abandoned his 15-year-old son; did young Will Riker end up in an orphanage or a foster home, or is a 15-year-old able to care for himself without assistance or state support on Earth in the 24th century?)
Crusher: Another only child, but, yes, both parents died, so more children may have been in the works. But they were working away from Earth at the time, and Beverly was raised by her grandmother off-world.
Wesley Crusher: The only child of Beverly and Jack Crusher. The premature death of Jack, a Starfleet officer, may have prevented any further children from being conceived. Was Wesley born or raised on Earth at all?
Troi: The younger child of Lwaxana and Ian Andrew, but she was not born or raised on Earth but Betazed, and Ian Andrew was a Starfleet officer, a hazardous line of work.
LaForge: Geordi was the child of
two Starfleet officers, and had a sister. Both parents survived to see their children become adults, despite the hazards of Starfleet duty. Yes, Silva LaForge did die, or at least is MIA, but Geordi was raised with two parents to maturity. How much time did he spend on Earth? Did the LaForge family often live on Earth? Probably not. Geordi spoke of moving often as a child.
Yar: Had a sister, both born and "raised" on a colony world, so their life stories tells us nothing about Earth family demographics.
Worf: Both biological parents dead, one biological brother, but they were
Klingons living on a
Klingon colony world, which, again, tells us nothing about typical UFP families. His
adopted parents, the Rozhenkos, did live into Worf's adulthood, despite Sergei being a Starfleet officer. We know the Rozhenkos had only one biological child, Nikolai, but they did not live on Earth exclusively.
Ro: A Bajoran, not born or raised on Earth, so not a sample of a typical UFP family.
Sisko,
Bashir,
O'Brien: see my post above, #38. I note that Miles lost his mother in 2368, after he was an adult, and that his father remarried within a year.
Dax,
Kira,
Odo,
Quark: not human, not born or raised on Earth, so not useful samples.
Janeway: The child or a Starfleet officer, killed in the line of duty, but whose mother lived into the 2370s at least. Kathryn had a sister. Did the premature death of her father, a Starfleet officer, prevent the conception of more little Janeways? Who knows, but the fact remains that the Janeway parents had only two children.
Chakotay: Again, not born or raised on Earth, so gives us no data on Earth-based family sizes.
Tuvok: Not human, not born or raised on Earth.
Torres: Half-human, but not born or raised on Earth, rather on Kessik IV, a colony world.
Kim: Known to be an only child, both parents still alive into the 2370s, neither parent a Starfleet officer.
Paris: I was wrong about this earlier (sometimes Memory Alpha pages aren't as helpful as they seem). MA says Owen Paris had at least two children, based on dialogue, so Tom may have had a sibling. Apparently Tom was born and raised on Earth.
7 of 9: Annika Hansen was born off Earth on a colony world, raised (such as she was) on a ship, then by the Borg. Another question of whether premature "death" (assimilated parents) prevented the conception of further children. Either way, the Hansens were not living on Earth and only had one child.
Neelix and
Kes: Not human, not born or raised anywhere near the Alpha Quadrant, much less Earth.
We have many more 24th century characters to study - 25 of them, though not all are human, and not even all the humans lived on Earth.
The 6 Earth-based families are the Picards, the Rikers, the Siskos, the O'Briens, the Bashirs, and the Kims.
We have 5 Starfleet families - The Janeway family, the LaForge family, the Paris family, the Troi family, and the Crusher family. May not have lived on Earth often or at all. The Troi family definitely did not live on Earth.
Of the 6 Earth-based families, the Picards had 2 children, and the Rikers, the Kims, and the Bashirs had only 1 each. The Sisko family is a hybrid, since Joseph Sisko had only one child with each of his wives. Only the O'Brien clan had more than 2 children. In this group, only the Rikers and the Siskos lost a parent on Earth when they were children. Miles O'Brien lost his mother after he was an adult, and his father remarried. Harry Kim and Julian Bashir had both parents still alive. Jean-Luc Picard had lost both parents by 2364, but probably to old age rather than accidents.
Of the 5 Starfleet families, 4 of them had only two children, and only one had 1 child (the Crushers). Four of those families lost the Starfleet parent in the line of duty; only the Paris family had the Starfleet parent live to see the child to adulthood.
My conclusion is that the Earth human population growth is probably negative in the 24th century, since in our samples there are more 1 child families than multiple children families.
Galaxy-wide, though, the human population may be, and probably is, growing, as there are many more colony worlds where prolific families
may be common.
...And a way to distribute the raw matter to the replicators as well. Maybe you're paid a visit by your friendly local raw matter delivery guy every month? Or there are 'pipes' connecting to the central storage.
What about direct transport, rather than plumbing or old-fashioned "milkman" type delivery? Either transporting the raw material directly from a central reservoir to a local household reservoir, or direct transport from a central reservoir to the household replicator on demand?