More in general, I've wondered where the tendency comes from to try connect every single dot. You know, Trelane being a Q, V'ger having a link to the Borg because it landed on a 'machine planet', Archer meeting Rasmussen (because, you know, they're both in the 22nd century), these two 'talking head' phenomena.
Don't get me wrong, it's fun to engage in such theories, but it also feels to me as 'small universe syndrome' cropping up time and again. The universe (and even the Alpha Quadrant) is vast; many things simply won't have a direct connection despite superficial similarities.
I don't consider making connections between things with several similarities and/or means of meeting, and which don't harm or affect the existing story in any way, to be "small universe syndrome," at least not in any negative sense, especially when done as fun fan speculation with little to no likelihood of it ever becoming incorporated into the ongoing franchise narrative. The shows and films use small universe syndrome all the time, so I don't know why people object to it so much when fans do it when there are literally no in-universe impact or stakes to it.
I consider the frequent use of "the Enterprise (or other hero ship) was the only ship in range" when it's in orbit of Earth and the crisis is dozens of light years away at Regula 1 and ideally there should be dozens if not hundreds of Starfleet or armed vessels of friendly governments or non-Starfleet agencies like the Fenris Rangers in the vicinity. Out-of-universe this is obviously done to get our heroes involved in the story, but they need to come up with a better excuse. In
TWoK they could have avoided the lazy "only ship in the quadrant" excuse by just saying the Genesis information was secret and compartmentalized and Kirk already knew about it so it made sense for him to go (plus, he had an established relationship with Carol Marcus, and she contacted him, so she would trust him), cadets or not.
I consider every captain having a close personal relationship or rivalry or extensive knowledge of every other captain (or officers in general) in a thousands of ships-sized Starfleet to be "small universe syndrome". Yes, it's not unusual for captains to come up together and meet each other at command officers mixers, briefings, or symposiums, or read about each other's exploits in reports and newsfeeds, but the sheer size of Starfleet, if the makeup of the fleets in DS9 are any indication, stretches the credibility of them being so close or knowledgeable about almost everyone they meet. Again, out-of-universe, this is done to have the captain or XO provide us with drama or exposition about the guest officer's exploits or reputation or their angry feelings toward them, but you could also do the same just by having them look the person's bio and command history up on the computer before meeting them (which they sometimes do).
I'm not advocating for all the things you mention above, but to use one example, you can find several similarities / possibilities between them:
Rasmussen and Archer meeting:
- Rasmussen was from 22nd century New Jersey and Archer from 22nd century upstate New York. They very easily could have met in childhood during school in a society with ubiquitous high speed air cars and maglev trains everywhere. Henry Archer was busy with the Warp 5 Project so possibly sent young Jonathan off to boarding school where he could have met young Rasmussen.
- Rasmussen was an inventor and probably truly had a doctorate degree from a technical university, so they could have met and been roommates (or been preexisting friends who went to school together) during their university years. Archer got a graduate degree in California, probably from CalTech or Stanford, though I'd lean more toward a technical degree from CalTech (both schools have a water polo team

).
- The Warp 5 Project was the biggest thing going for several decades for engineers and other scientists on Earth, so I could see Rasmussen trying to either get a job there or hock his inventions to get Earth Starfleet to "invest", and meeting Archer that way.
- The NX-01 was the only means to truly reach deep space in a short period of time for several years, so if Rasmussen wished to sell his failed inventions or ideas to other species, and needed a ride to get there, Archer's ship might be the only way to go.
- The latter two entries are actually enhanced if you have Archer possibly knowing Rasmussen beforehand from primary or secondary school or university, and Rasmussen using that connection to coerce Archer to get a job on the Warp 5 Project or to sell his inventions, and Archer turning him down because he didn't think his inventions were functional, safe, or reliable, This cause a rift between them and envy on Rasmussen's part as Archer's star kept rising and he toiled in obscurity. Perhaps he made Archer feel guilty when he requested a ride on the NX-01 and Archer obliged, but came to regreat it.
- Why was the future time traveling historian there in 21st century New Jersey in the first place for Rasmussen to take him out and steal his timepod? Could he have been investigating the personal history of Jonathan Archer, son of the Warp 5 engine inventor, first Warp 5 starship captain, hero of the Xindi Crisis and Romulan War, founding father of the Federation, future Federation President, and frequent time traveler and key participant in the Temporal Cold War which had become particularly hot during the temporal historian's time period (26th century)? Maybe he showed up and started asking (without revealing who he was) Rasmussen a bunch of questions about his friend and roommate Jonathan Archer, and Rasmussen got envious and angry and knocked him out in a fit of rage (or alternatively, he intuited that the guy was not who he said he was by the historian accidentally hinting at future information), and that's when he discovered his futuristic devices in his pockets, including his historical database and the remote control for the timepod.
- Maybe Rasmussen chose the Enterprise-D to visit because he was looking in the historical database to see what happened to Archer's Enterprise and saw the other entries for future Enterprises and that's where he got the idea to visit the Enterprise-D and steal their tech.
I could do some of the other ones you mentioned as well but that's enough for now.
There's not really much point to doing prequels visiting historical periods of Star Trek lore if you're not going to established some connections with the events, characters, species or tech of the future series. Not all the time, of course, but occasionally. Similarly, it makes sense for the future series to occasionally come across things that come from or reference shows set in their past.