Was Gary Mitchell and Kirk both ending up on the same ship a simple coincidence made possible by a small 23rd century fleet size?
Apparently not, as Kirk made specific mention of having requested Gary as his underling on his first command. We don't know if Enterprise
was this first command, or if Kirk had failed at first but succeeded in getting Mitchell on his second or third command - but we can speculate that the young and apparently steeply ascending career rocket Kirk could eventually get his wish, even in a Starfleet so big as to make this statistically unlikely.
Admittedly, there are other coincidences in Star Trek that might suggest a small force, even in the 24th century. But, say, Picard being familiar with a number of admirals and captains of large fellow starships is not statistically unlikely - because he is a highly positioned skipper himself, and his knowing other big names would be a sensible career-furthering skill. And Admiral Pressman reuniting with Riker, or Leyton reuniting with Sisko, would not be coincidences, but active measures taken by the empowered superior officers.
The one remaining coincidence that comes to mind is Riker knowing Paul Rice and then ending up searching for Rice's starship. On this occasion, there's no obvious reason why two officers from the same graduating class would cross paths again - unless Starfleet specifically assigned the E-D for the search of the Drake
after going through all the relevant parameters and finding this one convenient connection between the missing ship and one of the many starships within range.