Most importantly, the mission to divert the asteroid was intended to be a very short one. This could support your view - safe to leave a party behind for Kirk. Or, it could support mine - We will be right back, better to hasten and also minimize contact.
In The Doomsday Machine, the Planet Killer is apparently warp capable (no threat otherwise) but never uses the capability. Why is it creeping about?
In Balance of Terror we are asked to believe that an interstellar war happened with impulse-only ships. We are shown a 2 dimensional border of uncertain extent, which appears to be in deep space. Then a pursuit occurs at impulse speeds. And there is a comet with a tail... Where is the nearby star? Is this within a system that is unmentioned? Nobody bothered to define the limits of impulse speed except that it must be slower than light, so how could the Romulans present a threat to the warp capable?
In The Paradise Syndrome, the problem is purely one of real world astrophysics. The speed and distance of the asteroid are hard to make sense of. But. The basic premise of - short hop at warp speed equating to a months long crawl at impulse speed - is quite understandable. About the only case previous where this was brought up was Where No Man Has Gone Before - A line as I recall "Bases that were weeks away are now years in the distance." admirably explained the difference. Of course, that episode makes no sense anyway... There's an energy barrier around the galaxy nobody noticed before - but it is within a couple days of an automated production facility at sublight... I mean, we have to accept the barrier, but the location of Delta Vega is just a stones throw from it.
I do not find Salish's behavior to be a critical problem. He was suspicious of Kirok. He knew that nobody could enter the holy place without the password, though, so when everybody hailed Kirok a god, he had to be cautious.
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