The first point is basically "If the pragmatist didn't die, the plot couldn't advance." The part about him being painted as a jerkass should go, or at least be changed to an "often he's painted as a jerk so that the audience doesn't think too much about how sensible his suggestions are." He has to die because he's being sensible; he's usually a jerk so that the audience's gut reaction is to want him gone.
The second version is "Pragmatism sets up 'I Did What I Had to Do'". Again, he's often written as a jerk to keep the audience from thinking about how stupid the rest of the characters are being.
In making this division, we have to be careful not to overlap too much with Death by Genre Savviness.
"It's Occam's Shuriken! If the answer is elusive, never rule out ninjas!"True - but actually I'd see Death by Pragmatism and Death By Genre Savvy as being subtropes of sorts of Death By Sensibility
Sort of like Sister Tropes is what you're saying? Death by Pragmatism is when you're applying Real Life common sense, and die because that would make for a boring story; while Death by Genre Savviness is when you're anticipating the story itself, and die for being a smartass.
"It's Occam's Shuriken! If the answer is elusive, never rule out ninjas!"

This is something that's bothered me for a bit - Death by Pragmatism seems to have a bit a double-trope going on:
The article technically includes both, mainly due to strongly inherently associating being pragmatic with being intelligent and effective. However, it tries to play up "pragmatism marks you as death for being the selfish jerkass" while also trying to taut the "being pragmatic makes you the only smart person" bit as well, making the trope attempt an odd double meaning that doesn't work