Yes, but there's still a distinction between the model and the thing modeled. A map of your city is not the same as the city, even though the map is a real object in the same reality as the city.
Similarly, real numbers are a model that is instantiated in the brains of mathematicians, papers in the literature, etc. Those things are of course real objects. But real numbers are used to model lots of other real things.
My original point was really a comment on the way that the subject is often taught: the real number system is not introduced as some arbitrary set of rules that is as good as any other (though of course it is); it is introduced as if it were as incontrovertible an idea as, say… integer addition. I don’t think it is. It can perfectly well be argued that it makes sense and is useful, but its naturality is another matter. I personally find the leap from R to C less controversial than that from Q to R.
Yes. That’s why I said it’s a matter of taste.
My claim is that what makes things meaningful is how they relate to reality, and by reality I mean things like the three dimensional world and the passing of time we perceive. Whilst most of pure mathematics seems ridiculously abstract on first glance, I don’t believe there is a single topic that truly has no connection to reality.
> it's important not to confuse "reality" with our models of it
This is a frequently repeated point and I’m inclined to agree, but any such model also exists in reality and so it’s hard to know where to draw the line.