It's hard enough to score in American football when you have half an hour to score in. Trying to score when you have 0:30 left in the game? Nearly impossible, if you're on your side of the field.
The fundamental problem here is that the defense knows what's going on. They know you have 0:30 left, and need to get to the 30 yard line or so in order to kick a FG. If you're, say, on your own 30 - then you have 40 yards to go. So the defense just needs to make sure you don't get to the 30, but is perfectly okay with you getting ten or twenty yards - as long as you don't get those 40.
So you're left with the problem, particularly if you are out of time outs, of quickly getting those yards. You're going to run the ball? Might work, and some teams do. HB Screen pass actually is a bit better - lets you get the WRs downfield to clear out the safeties from the box. Or HB draw. That's better, except when it's mercilessly mocked of course. And it doesn't tend to work - maybe Adrian Peterson might knock in an 70 yard run, but more running plays end in fumbles than in 70 yard runs.
Specifically, there have been 68 fumbles lost in 9221 rushing plays so far in 2015. 3/4 of a percent of plays involve a fumble lost. This doesn't count plays that are aborted, either, i.e. fumbled snaps. On the other hand, there have been 23 rushing plays yielding 50 yards or more so far this year. 40 yards is a bit more, but still well under 68 - 43 plays total. And that includes many situations where the defense is playing more of a press defense - something they would never do with 0:30 left to go in the half. All that, and a rushing play that didn't go out of bounds would have to either score or leave enough time on the clock for a FG, right?
Okay, so we're not going to run - we're going to pass, right? Except, that's far worse. Rushing, odds are nothing happens. No fumble, no points, just a few wasted plays.
Passing, though, you have a big risk. When the defense knows you're going to pass, or at least is okay mostly ignoring the run because they can still play such that the RB gets 10-15 yards but no more, you have a lot more interceptions.
202 of these plays have been run in 2015 with 2:00 in the 4th or less remaining, down by a TD or less (but down), and 10 of them resulted in picks. 5% of plays like this result in picks. While most of those aren't pick sixes, that's often because a game-ending pick is brought out of bounds or just downed to avoid the risk of a fumble by the DB who picked it off.
On the other hand, only one was successful - Jameis Winston vs. the Giants - at scoring a TD, and ... oh, wait, no, that one wasn't successful either - the other team scored on a fumbled lateral.
Zero plays in that situation have been successful this year: because defenses know how to prevent them. Some probably have yielded a FG eventually - but it's not common, and it's much more likely to lose the ball.
Zone defenses are the main reason for this. Defense knows you have to pass the ball 20-30 yards, right? So they sit back far off the line, facing the QB, and everyone reads the QB's eyes. That makes it much easier to pick the ball off (rather than just running alongside the WR and trying to keep up with him). Zone prevent defenses are terrible at keeping offenses from advancing the ball 10-20 yards - and in a longer situation, 2:00 drill, they're actually pretty bad defenses. But with 0:30 left? Quite effective.
So - what's your call?
(Of course, as Bill Barnwell loved to point out, coaches still do run these plays... especially the basically pointless HB draws...)
On a side note, I think that the injury bit is relevant, though I suspect it's only because the odds of scoring are so low already. NFL teams have injury risks on every play, so it doesn't really make sense to try a play when you don't need to AND it won't give you a benefit. I think it would be hard to prove that coaches use this reason for kneel downs without asking them; but Bill Barnwell in the many Thank You For Not Coaching articles since 2013 certainly thinks it's relevant, and if he does, that's good enough for me.