There are thousands, probably tens of thousands of people out there who have built a 8-bit computer (usually Z80 based), according to schematics, from a microprocessor, memory chips, and a bunch of TTL chips. (I know there were at least twenty at my old school, and it was a small college.) It's one college class out of more than thirty, and by no means a replacement for college as a whole.
It used to be the case that MIT required their CS undergraduate students build an 8-bit computer from TTL (mostly 74XX) chips on breadboard in their Freshman on Sophomore year. (And no, we didn't even get a Z80; the most complex parts we got was an ALU unit and a 8250 UART so you could communicate with the computer over an RS-232 port.) It's really too bad that this isn't something which is required any more.
Instead undergraduates are taught how to write Java programs, which is one of those languages where it's impossible to worry about silly things like cache-line misses, because there are too many layers of abstraction between you and the hardware.... (And yes, you youngsters should get off my lawn, while you're at it. :-)
Do you mean 6.004[1]? I took that a few years ago and we virtually "built" a computer from scratch - laying down the wires with a hardware description language, writing a simple OS, etc. Unfortunately, it was all inside a simulator, so connecting the wires wasn't as tangible and satisfying as I would have liked. In the class, we heard that in the past students actually worked with physical components. Was still really fun and rewarding, though.
