One scenario that is important for me is melting snow. Adding snow to a narrow slot is painful and tedious. For this purpose I suggest that the flask opening has a shallow "U"-shape at one side (about 1-1.5 inch deep). This wider opening should make stuffing snow in there much easier, and you could also use the hip flask to scoop up snow directly.
It seems to me, that will just lower the volume of the flask. You should be able to scoop the snow perfectly as is, with flat opening. AFAIK, air easily pass through the not compacted snow (correct me if I'm wrong), so all you need is to drive the flask into a clean patch of snow, mouth first, and it will be efficiently filled.
No, it wouldn't. Snow is fluffy stuff: Out of 10 pints of new fresh powdery snow you make about 1 pint of water. Very hard, old snow the ratio is perhaps down to 5 : 1. Just driving the flask into the snow will gain you perhaps 0.5 oz of water, hardly anything at all.
You need to cram it, stuff it and compress it to get a noticeable amount of water in there. Melting snow is extremely tedious because of this. Sacrificing 1 oz of effective volume to gain a much wider mouth opening seems to me a very good compromise.
There's of course some tricks of the trade involved in snow melting. Starting out with a little bit of water, adding more snow so you don't have powdery snow, but some slushy water/snow mix is most efficient. You want as big a pot with as big an opening as possible. Melting snow in that cute little hip flask will be tedious to the extreme, to say the least.