In the original which set up the whole thing; they had very limited payroll; thus they could only afford to have one set of actors that you saw all the time regardless of how many were on the ship; also; the audience bonds with the characters they see all the time; thus if you ran it like the military would, the show would have had much less general audience appeal; it was the 60's after all; having the captian enjoy the charms of many women and spock hip to music and the like were all in fashion.
Oh man, that always drove me NUTS in TOS. It seemed so... illogical.
it drives me nuts as well and I don't know why would the Devs continue to follow this trend. I would perfer to have my Captain choose to stay on the ship once in awhile and then send number 1 with security to investigate.
If number 1 gets killed or captured you can send the captain to kick some tail...
...or get some tail when theres female orions present.
Look, the sad fact is that I barely trust my away team members to not shoot me or themselves with the phasers I have given them. No way am I trusting them to disarm a bomb or talk to someone on the ground.