An auxiliary coil also vastly increases the cost of an smps transformer because it will have to be hand wound (no machines can wind an off-line smps transformer properly and certainly not one with three or more coils)
So i ask why do designers bother with Auxiliary coils?
The shown application circuit serves a purpose. The designer apparently regarded an ausxilary winding as the most simple way to power the control circuit when the battery is shorted. Of course other options exist as well. They probably will use other part and don't fit an UC3909 datasheet.
I think, that most manufacturers would also contradict your opinion regarding costs of an auxilary winding. But if you can avoid it, it's better of course.
..i gave the above picture, but would like also to talk more widely about auxiliary coils, which i find always let me down at light_load and especially no_load.