Players who shot their jump shots from the free throw line:

[CavaliersFTW]

Guys who shoot their jump shot while at the free throw line:

Hal Greer - career 80.1%, 83.4% at best
Fred Taylor - career 59.2%, 62.4% at best

Who else? Is that it just two players in league history? I swear I've seen at least one other player who shot free throws that way but I can't recall who it was.

Any particular reason why push-shots are used instead of jump shots 99.9% of the time? Is it just because there's less moving parts?

[Im Still Ballin]

Because they are more accurate

Less variability with stable base

Curry has a fast release and skilled ball handling to compensate for his almost set shot like jumper. It's one of the reasons why he's so damn consistent shooting.