https://en.wikipedia.org/wiki/Peano_axioms#Formulation
To address the content of your post: I agree, but humans aren't purely logical devices created by Dr. Noonien Soong, and we do enjoy playing with things and joking about.
Not that there aren't mathematical reasons to start counting with zero, but this isn't a very strong one, at least not without further elaboration.
Starting at 0 is almost always correct, teaching people to start counting at 1 isn't. Why do we continually come up with convoluted workarounds simply because we educate children incorrectly?
P.S. Also fuckoff non-UTC time.
After a year of daily meetings with people on the east coast (of the US), London, Hamberg, and Brasilia from the west coast of the US I just moved to 24 hours and found it much easier to mentally calculate everyone's respective times- as long as I could keep the offsets squared away.
Screw daylight savings.
I can't even keep the offsets squared away since they shift a couple times a year.
Depending on who you ask, the natural numbers do contain zero. Notably ISO 80000-2 is of that opinion. In university, half my professors included 0 in the natural numbers, half excluded it.
For lists, starting them at 1 makes sense, but I would argue that's purely because that way the words "first", "second", "fiftieth" etc. line up with the numbering. It has nothing to do with human consumption.
For example floor numbers are made for humans too, but the European scheme of labeling floors -2, -1, 0, 1, 2, 3 makes much more sense than leaving out 0, leading to awkward -2, -1, 1, 2, 3, 4. Years are made for humans too, but most people are confused about the ordering of years because having the year -1 followed by year 1 just seems weird and makes date math difficult (for humans).
The seven-segment display inside the elevator in my former dormitory labelled the ground floor as '0', and the one below as '-1'. There was also a voice announcer, but I don't remember what it said on floor -1; I didn't go there often.
Elevators use 0 for ground floor, negative for basements, and positive for upper floors.
Just two examples of zero indexed lists in real life.
We also don't use negative numbers, basements are prefixed with a B, so B1 is like -1.