Here's three: 1. Counting *anything*
This is more a case where you restrict yourself to addition, and therefore never *need* negative numbers. But why would you want a type for which operator- is not defined?
I was neither supporting unsigned intergers nor supporting a type for which - is not defined. I was just pointing out flaws in the form of your argument. There are plenty of physical quantities that are always natural numbers and can be ridiculously large. For example, the number of microstates in a hot cup of tea. The unsigned integer might me useful if it asserted something on underflow to help the programmer debug, but barring that it's just a hack to save a bit. Refusing to define - on a numerical type wouldn't save anybody any trouble except the library writer.
Quantum states are solutions to equations. Those solutions are discrete and therefore countable.
Literally everything that can be represented on a computer in a finite space (e.g. Earth) is one of a finite number of possible values, so that line of reasoning is irrelevant.