Types do not inherently have any such restrictions. A value can belong to several types. In fact, if you posit types to have union, that necessarily follows.
If they don’t unless you add them to “explicitly remove such a restriction”, then that means you’re making types more set-like (set-theoretic).
In strict “type theory”, it’s the latter: types don’t have unions (in the sense that set-theoretic types do). There are sum types, which are different.