An IEEE I think article laid them out nicely into 4 categories:
Zero cost: what you put in microwaves, every cent counts.
Zero power: used to be obscure, the mobile market is of course making it very much less so, although those have elements of:
Zero time: speed is what counts, and plenty are willing to pay a hefty premium for it.
Zero units: say the military needs a CPU for a combat airplane which won't be made in more than 100s of units. Perhaps worth it for the prestige and getting the government to pay you to figure out neat things that might be usable in your bread and butter channels.
One modern example, but not with custom designs so much, is radiation hardened CPUs for space applications, a unit cost of say 100K is rather small in the bill of materials, the cost of failure in the high millions at minimum, could top a billion or billions, e.g. it would be very very bad if the computing subsystem(s) of the James Webb Space Telescope fail on its way to the Earth-Sun L2 point....