In classic Trek, Captain Kirk is unlikely to try to escape from a villain that has him under the gun and fail to do so. Sometimes he tries and succeeds. Other times he doesn't try at all, being led around by goons, defeated. (It's incongruous when this happens because we've all seen him get out from under the gun at other times.) How would this dichotomy translate into RPGs?
[This question is tangentially related to the recent issue of whether action movies, or other media in general, are good models for RPG mechanics.]
Most roleplaying games follow a simulationist model for determining whether a PC can get the better of a villain holding a gun on them. The player decides that the PC will go for it, and only then do the dice roll. Star Trek does not look like that. The Star Trek model would go something like this:
Player: I try to take out the guy who's holding the phaser on me.
GM: Roll for it.
Player: [rolls & fails]
GM: He's too alert. You know that if you tried it you'd almost certainly get disintegrated.
Player: Dang. OK, I go through the door like he's telling me to.
The player has tried to get the PC out from under the gun, but the PC hasn't actually tried (just like Kirk doesn't tryhe either does it or doesn't do it).
Now if the player's roll had succeeded, the PC would have taken out the villain with the phaser. Maybe if the player has failed badly, then the PC would have tried to take out the guy with the phaser and gotten beaten into unconsciousness, or maybe disintegrated. The less Kirk-like the PC is, the worse you can do to them with a bad roll.
Why would one want to use such a system? It would be to make the PC's more Kirk-like. That is, there's something base and demeaning about trying to do something and failing (especially trying to get the better of some mook and failing). Of course, whether Kirk takes out his captors or gets led meekly around depends on the needs of the plot, not dice rolls. But at least a system like this would let you look like Kirk while still using the roleplaying convention of dicing for success.
I'm not saying that having Kirk-like PCs is a good thing, or that I want to play that way. I'm just exploring how you'd handle Kirkliness in an RPG.