Well fact of the matter is unless one is carrying multiple pickets, a single picket is only useful for crevasse rescue or self belaying down a steep unconsolidated snow route unroped. I have done this many times. Or Very short roped, no more than 5-10 feet max between people. Of course if this is the case, carry a 2nd axe and go with the T-slot and girth hitch instead allowing more options, though descending soft snow a Picket is far preferable over that of an ice axe.
If one is going to place snow pro, one has to do so often; If your slip distance is over 15(30 foot run) feet on 45 degree snow face, one will rip out said picket no matter how hard the snow is and still go hurtling down the mountain taking your roped partner with you.
Pickets as snow pro, are psychological pro unless placed often in fairly hard snow. Same with ice screws unless placed very often in hard ice.
Its why most culoiur routes on steep snow/ice are mixed where a lot if not most pro is set in rock along said snow/ice route. Also done when very icy, so much lighter, better holding ice screws can be used.
PS. If in a group they can do crevasse rescue with ice screws/ice axe. Have to be in a larger group though. Unless carry 2 axes.
PPS. I biner clip my pickets. Got the biners along anyways, its not like you are saving weight by girth hitching the webbing through the hole and said webbing can easily get cut/worn out even if the holes are rounded.
PPPS. I go roped on steep snow because of crevasses, moats, not to hold my partners fall, as I already know I can't 50% of the time, even if short roped. We are talking 40 degrees plus here, below that sure you have a very high probability of stopping your partner, depending on conditions in my experience. Otherwise take the rope off if long snow sections, just means 2 or more will die instead of 1.