the preview with quick edit showed a correct pushback
It was just for pure chance. In fact, the very fact the generic QuickEdit start position happened to be in a better place, indicates that spot is not very common so, what is usually "wrong" ( the default QuickEdit position is not very useful in normal spots, as it is without any editing ), because "right", when used in a different context.
while the actual "to the right" pushback did spin me around 180 degrees (not 360, sorry). That's surely not mathematically correct to quickly throw my aircraft around and say "pushback complete".
That's exactly the opposite: because it MUST be mathematically correct, it would result in a bad *physical* representation, because when you add realistic mechanical constraints to something that would work from a purely mathematical point, in that situation it would result in a locked truck, because the IK couldn't be solve, similar to when jetways don't move if they cannot solve for the door.
As I've said, most of the times the automatic pushback can figure out a good solution, but this is not valid everywhere, and it's a combination of so many factors all added together: the length of the tow wheels axles, the towbar length if there is one, the distance between the front and rear gears of the airplane, the existing nodes in the airport and how they are placed, if there are nodes closer than the distance of the whole truck+airplane system, etc, etc. ALL of this is taken into consideration, but without mechanical constrains so, you might see 180s, but no lockups.
And again, for THOSE situation, it's where you need QuickEdit.