Young Simon (though not so young as me), I see you're as guilty as anyone of shortening your written words: "I'd" rather than I would.
Back on topic; there is really no need for anglers to speak of their quarry in such technical terms, it's pedantry and it'll never catch on and understandably so...... Will you be Leuciscus cephalus fishing this winter, no in all honesty I think you will be chub fishing.
It could be argued that using scientific names would reduce confusion but simpler to say a fishes whole commonly used name. Ron wrote: Bream - Albramis brama, this causes confusion; which bream species is Albramis brama common/bronze or the silver bream, if Ron had written common/bronze bream that would've offered greater clarity.
As for specialist groups using latin names, yes but I'd suggest more as terms of endearment. A few name changes pending: Barbel Society - Barbus barbus Society, Tench Fishers - Tinca tinca Fishers, these two include the species and not just the genus because in the UK we only commonly target that particular species but for mud-pigs I'll stick with the genus to save confusion; Carp Society - Cyprinus Society.
Can't see it catching on, but like said before, I can't see it ever catching on, use it where its needed.
Interestingly you mention anglers shortening fishes latin names, I'd say that's already going on, National Anguilla Club instead of a more accurate; National Anguilla anguilla Club.