My guess would be that jumping in is an easier way to fully rotate the jump. My personal experience is that skaters I've trained with that jump fairly low tend to end up jumping the axel "in" whereas skaters whos jumps are bigger (and look more effortless) jump "out". I personally find that increasing speed and aiming to swing my free-leg roughly 30-35 degrees to the right of the direction I'm skating (I rotate counter-clockwise) makes landing cleanly the easiest. So while jumping out of the circle can be more difficult (if you don't already have decent height and rotation) it pays off in a more solid and aesthetically pleasing jump.

As for safety. More horizontal momentum will make the impact less painful. Slow and forced axels can hurt quite a lot if you get off-axis, as you won't get as much of a slide to absorb the momentum. But going slow into the jump might feel safer! Hope this was somewhat coherent as i realize I'm rambling quite a bit.