The 74181 was a really cool classic part, and was used in a lot of discrete CPUs.

Unfortunately, it's one of the parts that never made it past the 74LS family. :(

But... on a purely philosophical note, are you really building a CPU from gates if you use a '181?

With that said, the capstone project for my college electronics course was to build a 4-bit computer from 74LS chips, and we used the '181. The instructor explained that it was a necessary simplification, in order to get the project into the space and time available. We were provided with the schematic, but were expected to get it working with little or no help, and to demonstrate operation of a program. I wrote a dice game.

Not true...Philips did at least a 74F and 74HCT version, and TI did a 74AS181. Weirdly, Hitachi did a 74AC182 (lookahead carry generator for '181), but AFAIK only the 74HC181. Never figured that one out. There's also an ECL version (MC10181).

If you jumped to the 74381 you could get nifty things like the IDT7381 or L4C381, which are the equivalent of 4 '381s in a PLCC package that ran at a 25ns cycle (faster, I think, as well).