Earlier quoted context omitted.
Don't make this about me. Read the history of math & tell me what conclusion you come to when you see people making algorithms, essentially, for dealing with natural processes.
Of course, as long as you stay in the realm of measurable things. However, we still need to explain how and why the perfect abstract mathematical objects are of any use in the real world (as opposed to other abstract objects such as patonician ideas, or more commonly gods).
Well neither of those two deal with counting... We already know (historically, empirically) that counting & manipulating 'stuff' is what works for making applicable theories. Mathematical abstraction preserves those "traits", & makes the object more general - ie more flexible. Chess for example is about counting, but it's not explicitly written in a form that allows you to drop it in a theory.
I think the important thing is the traits aren't arbitrary. They were forced on people, eg you need to learn counting if you want to keep track of your goats.