In every Trek series from TOS to even the reboot 2009 Trek the ships have meant a lot to each commander.
Which doesn't mean they would be entitled into thinking these are "their" ships. Their employer still owns them down to the last rivet.
However, in TOS we only observed a single mission (lasting five years); in VOY, we saw a stranded ship. Transfers no doubt would have followed at the conclusion of these events, but we're biased because of the nature of what we saw. Sisko in turn went through ships like changing shirts; it's just that the Defiant
was a bit tougher than the others and lasted longer.
It's really only TNG that shows us a truly unrealistic case of the same people being stuck on the same ship for the better part of a decade, and in some flash-forwards even longer. We did see two attempts to get Picard off the ship, and three to get Riker to move forward, but these came to naught. Yet Picard was explicitly positioned on the top ship of the Federation. Kirk, for all his reputation, never seemed to operate anything more than a run-of-the-mill cruiser - no "flagship" nonsense, no preferred status. He shouldn't have been protected from realistic crew transfers...
...And he wasn't. He was off the ship as soon as TOS ended, apparently. And back only because he wrangled some Starfleet arms. And then off again. And then back for a birthday joyride. And then
he could only get back by committing theft and treason. Hardly an example of the standard Starfleet way of treating transfers.
Unless I'm misremembering the film, there is no hint that she is armed. Just that she is supposedly fast and has a tractor beam.
We can see that the ship has all the guns mounted; those are a visible kind of detailing. And we can see she's painted pretty and all. Starfleet finished
that ship apparently before fully testing whether transwarp worked.
...Although only if we assume that transwarp did not
work. And we have no real reason to assume that. For all we know, transwarp was already a splendid success, NX-2000 was the sixteenth vessel to successfully enter transwarp in 2273, and she was subsequently fitted with full operational gear such as phasers, while ten of her sister ships were doing their pre-commissioning trial runs or maiden voyages.
And Scotty just happened to be way behind times and dead wrong in his professional estimate. Which isn't much of a wonder, considering how he apparently voluntarily got stuck on an ancient training ship instead of doing any proper engineering work in the 2270s or 2280s.