But whether standard software is able to express this system is up to the software, not the system, no? Why is this way of timekeeping weird, apart from the arbitrary decision not to support it?
I object to the latter since software is not the source of truth, the social practices it aims to encode are. It is perfectly reasonable to say that this particular practice is so rare that it is out of scope, but this makes tzdb a not quite correct approximation of reality, rather than reality an approximation of tzdb.
There are people who want to end any other human to ever live homeless in starvation or any kind of poverty and there are people who want to eliminate anyone they judge as threat or a nuisance while reinforcing there feeling that they dominate everything that will ever matter in the world and the rest.
Software can help all kind of purpose.