Some student travel cover applies to trips to countries around the world, but that does not mean every destination or every circumstance is covered without limits. Government travel advice, destination rules, and the terms of the policy still matter.
Another important distinction is that “worldwide” does not usually mean “in your home country as well”. Many travel-style student policies are built around being outside the insured person’s home country.
So yes, the cover can be broad geographically, but it is still controlled by eligibility, destination conditions, and policy wording.