parking spot, that you saw was clear as you prepared to back in, is much faster than backing into typical parking lot traffic. If you are backing into a wide open and empty area with no other cars or possible traffic, it might be faster to back out... but that is not realistic for most parking lots.
When backing in, you naturally drive past the spot, see it is clear, then back into an open and clear space. You also have the best visibility when leaving that space.

If you pull forward in, sure parking is just as fast, but pulling out you have to go much slower and open yourself up to far more potential hazards and accidents.