Wire wrap done correctly requires wire wrap posts which are getting quite rare these days.
Huh? Standard WW posts are 0.025 inch square posts, which are still pretty common. I didn't THINK that there's a difference between WW 25mil posts and other 25mil posts! (theory says that the corners of the post bite into the wire, forming a reliable (gas-tight!) connection. So I suppose that WW could require posts of increased "hardness.")
I had a summer job after HS that consisted mostly of wirewrapping prototypes...
Wirewrap is NOT "quick." If you can do 30 connections an hour, you're doing pretty good. (including measure, cut, strip, wrap one end, route, wrap the other end.)
These days, WW is depressingly expensive, having become a "slightly supported niche" rather than one of the mainstream techniques. The hand WW tool that used to be $10 at radioshack is now $30, and a 40-pin WW socket will set you back more than most 40pin chips (about $6.) (actually, it was never cheap. Those lovely WW panels you see occasionally cost a small fortune; but back then chips were a lot more expensive, too.)