If your code compiles in ~16 seconds, reducing that to 4 would add comfort.
If your code compiles 60 seconds, reducing that to 15 would allow not losing concentration.
If your code compiles in 60 minutes, reducing that to 15 minutes would actually allow to do any work on that (not that it's not possible, but it's really not pleasant).
I thought about 4-core vs newer 8-core desktop CPUs when upgrading, but decided that I more often do work on less than 4 cores (with 1 you get the "Turbo" capacity). The only multi-threaded program is PyCharm which can use up all those cores when recalculating its static type checking of Python code (which it seems to do quite excessively).
Another thing useful for a programmer is being able to benchmark things - with a multicore machine you can tie off one core (or multiple cores!) exclusively for a benchmark, which can really help reproducibility.
Show them the numbers, make it an easy decision for them.
I wouldn't call it "hacked up", but large-area surveillance radar systems like AEGIS and JSTARS use very high density systems like this, because the size, power, and cooling available for the signal and display processing are severely limited. Same can be said for systems like the mobile Doppler radars the National Weather Service and various universities use for studying severe weather.
Another idea: you can also do some big linear algebra problems. I'm doing this now at work and it's kind of interesting that a single cloud machine is like a supercomputer from a decade or so ago (32 cores, 128 GB of RAM). I guess that is obvious but once you start using the whole machine it becomes impressed upon you.
I actually bought a big Dell machine to do secure builds... thinking of getting something like this though :)
Raytracing alone can load absolutely any system to the max, because it scales so well.
And that's just my born in Computer Shopper Pavlovian response to articles about new more powerful CPU's. I have no idea what I would do with eight fifteen core CPU's and six terabytes of RAM other than write checks to Alabama Power and think of ways to mention it in casual conversations. I mean a 911 Turbo? at least I could use it to pick up hamburger buns.
At a deeper level, I always wonder, what [besides mining bitCoin] would other people hack up with a monstrous amount of computing power on the order of a data center in a container?