I can answer some of this, but others may have more complete answers. Several factors come into play:

1)The two potential hybrids would have to bloom at the same time.

2)They would have to be equally attractive to the same pollinators

3)Pollen from a different species will often grow slower down the flower's pistil(s) than the species pollen (i.e. if a red raspberry flower has both red and black pollen on it, the red pollen will 'outcompete' the black pollen.

4)Some crosses only work in 1 direction (for the red X black raspberry cross only one of them can successully act as the female parent. [I can't recall which one].

5) Cross species hybrids seed germination and seedling vigor is sometimes(often?) less than the non-hybrid seedling

6) They hybrid's are often sterile themselves.

Don't confuse terms like "Hybrid" corn with cross species hybrids. Hybrid corn refers to a cross between two 'landraces' (inbred strains) of corn that the cross between them results in a strain of corn w/ hybrid vigor. In this case both species involved in the cross was Zea mays. In cross-species hybrid is another ball of wax.

Actually, in the wild there has actually been a fair amount of accidental hybridization in Rubus. While Rubus was largely a forest margins type of plant in its natural habitat, the spread of human beings across North America (and presumably elsewhere), clearing land left and right, allowed formerly isolated species to come into routine contact with each other. While not necessarily the norm, hybrids between blackberry species are not phenomenally uncommon in the wild.