How about the species that are only in captivity for captive breeding programs? I guess that doesn't count right? I think it would be hard to say exactly, as the 'list' would keep changing.
Regardless of no more export/import, there are species in the pet trade now that were unavailable in the past. As more and more rare species are having their numbers multiply in captivity, breeders are now letting them go into the mainstream pet trade, such as Griffin my Ruppell's Parrot, and a good amount of other species nowdays.
Without googling it, isn't there 300+ parrot species out there? I'm not sure what percentage of those are even in captivity, but I'm willing to guess that out of the species that are in captivity, the majority of them would be available in the pet trade, though some not easily found.
A couple of years ago, I seat thru a presentation by an author of a book written about the passenger pigeon. That person was an admitted writer, who combined newspaper accounts and other non-proofed documents to create the book.
There is no question that a bird that existed in the numbers presented and now (1914) no longer has living representation is a sad statement. Having said that, the numbers used as part of the presentation and book really did not add up, nor did the distances traveled with in 24 hours for a bird that had the flight design of a freight train box car. Even if the passenger pigeons used the back or front edge of storm systems to push them North/South in the flyway(s). The rate of travel is just not a reality. If one where to apply the numbers provided; there would have been 'dead zones' resulting in their foraging and roosting areas as they migrated in the Spring and Fall. There was just so much questionable information it left me wondering what if anything was founded on the truth and not just the expanded statements of a newspaper editor's want to sell papers.
Once again, there is no question that the lost of the passenger pigeon is a hole in North America history. The passenger pigeon's story really needs a proper and honest presentation. There is no question that the number of passenger pigeons was huge and their loss rapid. Beyond that is history that needs an honest presented.