I don't regard Kirk being down as a plot-hole. IMO Kirk was more equivalent to say Captain Cook, discovering and exploring - making 1st contacts. Captain Cook didn't stay on ship, he went out and 'discovered' Australia and uhhmm Hawaii. And if sometimes you get killed by the natives because you didn't stay safe on the ship then that's a risk you take.
Also Kirk tells Spock several times he has to 'feel' the situation. So its Kirk's style to beam down and assess the situation to judge the safety for his crew and the Federation.
Terrell probably beamed down because he and Chekov would have to convince Marcus that the planet was suitable. Marcus wasn't going to accept second hand reports.