I think that this is not quite true: there is such a thing as mathematical impossibility in the real world, but it applies only to mathematical models; that is, models cannot exhibit the behaviour. This doesn't prevent the real world from exhibiting that behaviour, but it does mean that, if the real world exhibits that behaviour, then the model is inaccurate.
These caveats might make the notion seem useless (as you seem implicitly to be arguing), but I'd argue that they are quite useful. The whole pursuit of quantum gravity comes from the realisation that relativistic and quantum mechanics are mathematically incompatible. That fact alone doesn't tell us which one, if either, is correct, but it certainly tells us that they can't both be correct in all regimes, and that's indisputable information about the real world that we wouldn't have without idealising it through mathematical models.
By the way, did you edit your post? I thought the post to which I responded only had the sentence above, but on preview I saw:
> If it's impossibility is evident in a mathematical model, that's still physical impossibility.
This sentence I don't understand at all. I would argue instead that there is no such thing as physical impossibility; the real world will do what it likes, and we may not forbid it, only observe that certain things haven't happened yet. Any impossibility we observe in a mathematical model is, I would say almost by definition, a mathematical impossibility, even if we deduce physical consequences from it.