I also found it odd that Leela and Fry didn't even attempt to make a run for it when that guy randomly announced that they were slaves.
I once mentioned something similar:
They basically have an armed spaceship and lots of weapons at their disposal. Equipment with which anyone of the trio could single handedly conquer a whole planet similar to ancient Earth.
Of course parodies need to stretch reality by quite some margin for humor's sake. Yet, as a tabletop wargamer, I am prejudiced and usually demand combat/battles to follow some rules. "Galaxy Quest" was a good example..it was goofy, it was hilarious...yet, the fighting scenes had structure, and did not randomly follow the plot demand. Up to the great showdown: Sarris
: You fool! You fail to realize that with your armor gone my ship will tear through yours like tissue paper! Jason Nesmith
: And what you fail to realize is my ship is dragging mines
Futurama often lacks in the department of well-developed kick-ass action scenes.
(Which is also a reason for my dislike regarding Leela: A female combatant in a universe with the strict rule "A man may NEVER successfull beat a woman" takes away quite too much of the tension and interest of a fight. Either write her e.g. like Deunan from Appelseed or like early Lady Death, or keep her away from the front).