As a general rule of thumb: Never use static material only as protection while moving.
Unless you anyway know what you do, I suggest you stick to that rule. There are several examples of fatal accidents involving static falls of very short distance into your binding, which then broke. Fall factors are not a factor to consider, as this compares length of fall to length of rope which will dynamically brake, while here there is nothing dynamic. Even if the material holds, such a static fall causes injuries or at least severe pain in the hip region (I know, I once fell about 0.5m into a daisychain while aiding, two connections ripped and thus damped the fall, it still hurt a lot and caused me to abandon the climb.
However in the exact case shown above when slipping, you would not fall directly into the sling. Scraping over the rocks you would not be very fast when the sling stops you, so it would not be comfortable, but hardly hazardous.
Still the best method in such terrain would be going on short rope. If properly done and trained you are safer and faster than with such improvised protection, but it really needs some practice. You are connected with about 10m of rope and the stronger climber goes ahead. In very easy and hardly exposed terrain you simply go simultaneously managing the rope so that it does not get in the way. On slightly harder or exposed terrain the leader places the rope over spikes on the go, thus providing security against falling off completely. In case it gets much harder you secure the second (e.g. wrapping the rope twice around a suitable spike) and you climb the section, then you belay the second up with again a spike or shoulder belay (this is a direct translation from German, no idea whether it is the correct term in English).