How likely are the Sonnenschein-Mantel-Debreu results?
The space of economies can certainly be modeled as a measure space. Perturbing an economy (the parameters of preferences and production functions) generally changes the excess demand function continuously, so if there is one economy with a "weird" excess demand function (however defined), then there is a positive measure of them (open ball around the one weird economy). 

As the number of commodities grows, and preferences for each new commodity are randomly drawn from some space, then my intuition is that the probability that at least one commodity has upward sloping demand converges to 1. The probability that all commodities have "weird" demand likely converges to zero. 

Empirically, upward sloping demand is rare (examples of inferior goods are rare).