Now, before you curse his name, hear him out, okay? Lempel explains that "there are a few reasons" you won't see Trophies on PSP and, chief amongst them is "keeping it secure." See ... the PSP has been hacked. A lot. Like, a lot a lot. Lempel says that "if people can artificially inflate their rankings and amounts of Trophies" via the PSP on a shared PlayStation-wide Trophy system then it "kills the whole [Trophy] system," PS3 included. So "keeping it secure, keeping it fair" is the best solution – but that means no Trophies on PSP.
And, since the PSP has that same promised 10-year life cycle (as evidenced most recently by the PSP Go) it'll be some time before we get an entirely new (and ostensibly secure) PSP platform upon which a functioning Trophy system might be grafted. See you in 2015!