I used to never build it but in the last month I've been randoming Civs to get out of my comfort-zone of Tall culture/science victory, and I've found it's very powerful.
I agree that it's very good if you can get all the barracks and then just sell them off, but you make a very good point about how it's weird that you make all your cities create veteran units, then you build it, then you build all your units in one city. I'd say it should be changed to a different effect but since it's so early (the EARLIEST national wonder, actually), maybe not.
I also agree that NIA is terrible/not worth the effort. It needs a buff or possibly be changed to a building that only requires constables. Hermitage, on the other hand, I build almost every game... That's probably more of a personal preference thing, though. For some reason, I simply love getting social policies, so end up building a lot of culture buildings even when I "shouldn't"... Hermitage is also pretty powerful. As a side note, I have never used religion to buff it, in favor of other bonuses.
I also want to put my vote in for the 75% requirement for NWs. It's so annoying to sleep a settler on a tile until you get the wonder, whereas before I could prepare by buying/building the required building in another city.
BUG:
And rhammer is correct, "Training" has no dependencies, despite the display in the tech tree. I think I just skipped it completely in my Gandhi cultural victory =P