I'll at least put forth that there are those who disagree that the BSC is in "dire straits" outside ornithology. It is true that, at least in North America, herpetology has seemed to have completely taken on the PSC, and as Morgan mentioned, mammal taxonomy seems to be on the fence.
But in the realm of arthropods (disclaimer - not totally my discipline), I've seen very little detraction from the BSC. While many species can be visually similar, so many work under a "lock and key" mating system that the criterion of "do they or don't they breed?" is very straightforward - lending itself well to the BSC. In addition, insect dispersal is even more fluid and long range than avian, so genetic-based phylogenies quickly get messy with hybrids unless there are real separation mechanisms.
In botany, BSC is fairly robust as well, although nonuniformity exists. I'm not aware of many major PSC/ESC pushes for plants, and again they are taxa that more or less lend themselves well to discrete breeding units, albeit hybrid questions are certainly more complex than with arthropods. There are even many cases in which "sub-BSC" taxonomy is tolerated - for example there are goldenrod "species" which have two forms with different chromosome counts and as far as is known, the forms cannot breed. However, in every other discernible way they are identical. I won't even start with fungal taxonomy.
From what I have seen, PSC has been adopted most enthusiastically with taxa that have more limited dispersal - herpetology, riverine freshwater fishes, terrestrial/freshwater mulloscs, etc. and perhaps that is its most appropriate use. But I'm not quite convinced that its taking biology by storm.
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