For once I disagree with you Wally, the maths may well prove your point, but what about the co-efficient of friction between the ladder feet and the point of contact?
Under normal conditions there is no need for a 'ladder footer' as the rubber ladder feet will not slip on a dry firm surface such as concrete, brick etc.
Introduce a film of moisture and the situation changes completely. No amount of downwards pressure will alter the co-efficient. In this case you need a horizontal resistance (the ladder footers feet) to arrest the outward (away from the wall) tendency for the ladder to overcome the co-efficient and start to slide.
Admittedly the ladder footers feet are also subject to the same problem, so perhaps footing is a useless exercise anyway.
I always look for some sort of solid 'restrictor' - wall, hollow in the surface, edge of raised paving slab etc which is not affected by the above.