There are many more things other than aim assist present in any aiming system. Aim assist is usually just the gradual deceleration near or on opponents, destiny has an extra auto-aim feature present which seems to be at fault pulling ur reticle off point The assault rifles got a minor nerf to the aim assist after they got patched if anybody noticed. They can weaken the effect, but it can and will turn many players away...
Aim assist is used to balance guns. Turning it off would probably break everything.
You would get wrecked if you had 0 aim assist. Possibly they could have a lower level of it, because it's VERY agressive compared to something like cod. But, if aim assist is in the game at all you'll need it to be competetive.