Don’t know about appeal success. But FWIW I do recall that a friend of D2s took a leave for academic reasons.
He did come back and he did finish. So it isn’t necessarily the end of the world.
I myself had a friend there who struggled there, and never stopped struggling. He had a miserable four years.
I think he’s happy now that he stuck it out . But myself, I don’t think it should be that tough.
If you do wind up taking the leave, suggest do exactly what they suggest:
“address the deficiencies in your academic performance and to re-examine your goals and priorities”.
Counseling may help you figure things out.
Maybe you need better study/work habits.
Maybe you need a less mathematical major, or an easier school.
If you take the next semester math & physics at a community college, maybe that can help reduce the amount that you are falling behind academically, and also boost your GPA… Which might help if you decide to transfer someplace.