This buys you the 7 yards of a snap and eliminates any chance of blocking the kick. On top of that since its a free kickoff and there's no onslaught from the defense, you can wind up and kick a monstrously long kick. The most recent attempt was 69 yards and missed by very little.
I'm not suggesting it has any particular place in the modern game, but these are some of the reasons coaches might elect to use it at the end of a half.
You can, but the benefit here is that you have a shorter kick and no one in front to block it.
Did you read the bottom of the Wiki page? Apparently Detroit was in a position to try a kick like this from the 42 yard line, but opted for a regular field goal kick instead of the free kick. This meant their kicker had to boot a 50 yarder instead of a 42 yarder. He came up short…
It’s an interesting rule. I like the crazy rules like this one. They’re part of what makes the game so fun!