How come we never see anything physical that behaves like any of of the non-standard models of first order PA?

Umm... wouldn't they be considered "standard" in this case? I.e. matching some real-world experience?

Let's imagine a counterfactual world in which some of our "standard" models appear non-standard. For example, in a purely discrete world (like the one consisting solely of causal chains, as EY once suggested), continuity would be a non-standard object invented by mathematicians. What makes continuity "standard" in our world is, disappointingly, our limited visual acuity.

Another example: in a world simulated on a 32-bit integer machine, natural numbers would be considered non-standard, given how all actual numbers wrap around after 2^32-1.

Exercise for the reader: imagine a world where a certain non-standard model of first order PA would be viewed as standard.