I am not trying to be funny. It seems to me that you are misunderstanding the usage of the word zero in this context, as in absence of any. Synonymous to "no", as in "no threes".
It is not about the number 0.
It is not about the number 0.
The example in the question is:
> For example, if we choose two 2s, zero 3s, and one 5
That's talking about "zero 3s", not "three zeroes".
In this context "zero" is not a noun, but an adjective.
In addition, see the adj. definition of zero: https://www.oed.com/dictionary/zero_n?tl=true#1209971660