That's what I would expect most mathematical-existence types to think. It's true, but it's also the wrong thought.

Wei, do you see it now that I've pointed it out? Or does anyone else see it?

I take this to be your point:

Suppose that you want to understand causation better. Your first problem is that your concept of causation is still vague, so you try to develop a formalism to talk about causation more precisely. However, despite the vagueness, your topic is sufficiently well-specified that it's possible to say false things about it.

In this case, choosing the wrong language (e.g., ZFC) in which to express your formalism can be fatal. This is because a language such as ZFC makes it easy to construct some formalisms but difficult to construct others. It happens to be the case that ZFC makes it much easier to construct wrong formalisms for causation than does, say, the language of networks.

Making matters worse, humans have a tendency to be attracted to impressive-looking formalisms that easily generate unambiguous answers. ZFC-based formalisms can look impressive and generate unambiguous answers. But the answers are likely to be wrong because the formalisms that are natural to construct in ZFC don't capture the way that causation actually works.

Since you started out with a vague understanding of causation, you'll be unable to recognize that your formalism has led you astray. And so you wind up worse than you started, convinced of false beliefs rather than merely ignorant. Since understanding causation is so important, this can be a fatal mistake.

--- So, that's all well and good, but it isn't relevant to this discussion. Philosophers of mathematics might make a lot of mistakes. And maybe some have made the mistake of trying to use ZFC to talk about physical causation. But few, if any, haven't "noticed the difference in style between the relation between logical axioms and logical models versus causal laws and causal processes." That just isn't among the vast catalogue of their errors.