Imagine building a full size sleeping wood platform for 2 above the snow with just a folding saw and a knife, it will take half of the day or more. With a long axe - an hour and half - max.
Actually, I do have a hard time imagining a sleeping platform for two above the snow. I would prefer to erect a tent, possibly even a floorless model. I will be warmer and it will take less time. I'll bet a proficient person can build an igloo in about an hour and one half(I am not that dude) and that will be even better. If you snuggle down in the snow, the temperature will be about 32F, while if you are suspended above, you will be subject to whatever the ambient temp might be...-40F?
I, too am a fan of the Sven saw. A spare blade weighs much less than a sharpening stone. But let's face it, if weight is not an issue, that is, if you are not backpacking, carry all of the above. There are good reasons these different tools have been developed. Both saws and axes go back to the Stone Age.