If in axiomatizing arithmetic we are ontologically committed to saying that 1 exists, 2 exists, 3 exists,etc., then we may say that there are numbers even if it is not axiomatic that 1, 2, 3, etc. are causally inert, nonphysical, etc.

I'm still lost here.

Instead of being a platonist and treating numbers as abstract, you could treat them as occupying spacetime (like immanent universals or tropes), you could treat them as non-spatiotemporal but causally efficacious (like the actual Forms of Plato), or you could assert both. (You could also treat them as useful fictions, but I'll assume that fictionalism is an error theory of mathematics.)

I'm not sure I would say Plato's forms are causally efficacious in the way we understand that concept-- but that isn't really important. Any way, I have issues with the various alternatives to modern Platonism, immanent realism, trope theory etc. -- though not the time to go into each one. If I were to make a general criticism I would say all involve different varieties of torturous philosophizing and the invention of new concepts to solve different problems. Platonism is easier and doesn't cost me anything.

I think many of the views on which mathematical objects have some causal (or, if you prefer, 'difference-making') effect on our mathematical discourse are reasonable. The views on which it's just a coincidence are not reasonable, and I don't think abstract numbers can easily escape the 'just a coincidence' concern (unless, perhaps, accompanied by a larger Tegmark-style framework).

Ah! This seems like a point of traction. I certainly don't think there is anything coincidental about the fact that mathematical truths tell us things about physical truths. I just don't think the relationship is causal. I believe causal facts are facts about possible interventions on variables. Since there is no sense in which we can imagine intervening on mathematical objects I don't see how that relationship can be causal. But that doesn't mean it is a coincidence or isn't sense making. I Mathematics is effective because everything in the natural world is an instantiation of an abstract object. Instantiations have the properties of the abstract object they're instantiating. This kind of information can be used in a straightforward, explanatory way.

universals occur exactly in the spatiotemporal locations where their instances are, and they are exhausted by these worldly things.

This is a particular way of understanding universals. You need to specify immanent realism. Plenty of philosophers believe in universals as abstract objects.