my opinion is that snap is always important, what ever punch is thrown. Snap is coming from hips. Harder you rotate (or violently how grey said in one of his posts) your hips the more snap you will get. If you do that without hips then you are punching from shoulders. You can get snap from shoulders, but the power of punch is very small, its used like a tactical weapon, not to hurt.
I think were on the same subject, Power comes from your centre of gravity. Move from it, balance is lost, its all position.
,,,this is two different puncher at different distances from target ,,every punch you throw in boxing can be long or short range Punch's ,,,,practice both Punch's then move on when you have understood what ,were & when to throw the correct shot
There's different kinds of hard punches. Sharp precise ones (Mayweather), ones that catch you moving into them or clip you (timing), crushing ones that just overpower you(force/strength...Tyson), snapping ones that kind of have the baseball-off-the-bat effect (SRR-Fullmer), etc. Then there's guys like Arguello/Monzon/etc that just have a heavy-handed sort of power that feels more damaging when it lands. So just hit the guy somehow.