yes squatting down is natural, but putting heavy weight on your neck then squatting down is totally different if you have relatively long femurs your balance will be all messed up, which of course makes it ineffective because its an awkward movement to do.
Now with leg press, its like squatting on some planet which has higher gravity, its practically squatting without the awkwardness of your upper body being pressed down against floor, all of the focus on the legs.
the best thing would of course be to have some sort of belt that could hold weight and you just squat down or something.
And deadlifts are more natural than leg press again, who squats down to pick up stuff from the ground honestly? you bend over pick something up and straighten yourself up again, aka deadlift except what your picking up is damn heavy.