The purpose of interning things is to be able to compare them by comparing their memory address; you ensure that you never create two objects with the same value (when the program requests the creation of a second object with the same value as an existing object, it instead receives a reference to the pre-existing object). This requires that the things you're interning be immutable; if the value of an interned object could change, comparing them by address isn't going to work.
In Python, it's not possible to enforce the immutability of user-defined class instances, so it wouldn't be safe to intern them. I suspect that's the main theoretical reason intern doesn't cover class instances.
Other built in immutable types are either comparable in a single machine-level operation already (int, float, etc), or immutable containers that can contain mutable values (tuple, frozenset). There's no need to intern the former, and the latter can't be safely interned either.
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