One would wonder what the government would stand to gain from killing a nameless man who stood in front of some tanks, delaying them for a few seconds.

Going to stop you right there. They did it because they needed a moment of individual brutality that makes the audience feel bad for the people the villains are oppressing, so it is satisfying when the heroes go in and stop the evil dictatorship at the end of the movie. I would've preferred if they showed a scene with tank man's loving family before he was brutally killed to inspire the good guys, but they probably had to leave that on the cutting room floor so the overall flow of the scene worked better.