One other thing..It all depends on your goals.
Hardstyle swings seem to have more carryover to deadlifts than anything. I've also heard folks comment that hardstyle swings had ill-carryover to the barbelll lifts because someone doing them pushes the bar out...I think it will depend on the athlete.
I'm a KB Lifter. My goals are to lift the KBs for very high reps. So, my focus has been on technique that allows me to do that. Not everyone will have those aspirations, but I still feel the version of the snatch as I teach it (and what is taught by some of us or thought of as a fluid style) is athletic and it teaches timing and requires the athlete to be aware of where their weight is..that kind of thing. Other things do that...But, when I was heavily entrenched in the RKC...none of that stuff was covered. Their goals are different. Snatches (and Jerks are not taught in the level 1) are just one of several exercises. They have a different focus. Our focus in terms of KB usage is simply high reps.