Standard disability insurance protects against job loss in the case of a disability. The benefit is based on income. No income no benefit. The income is a defined insurable interest.
I would guess that the insurance for medical students is maybe a special lines insurance or any offering through a professional association. There is probably the volume and practice of offering it. With such a low premium it is probably tightly written and used rarely.
Celebrities can insure their legs, abs, fingers etc. it is typically done by lloyds of London but alas our budding kids would not qualify as they are not famous yet.
I work in finance and insurance and would say not too bother. I don’t think you have a defined insurable interest yet. But you are free to correct me if you find an insurer.