I don't read the Turing test as being designed to prove "intelligence" at all. It's an assertion of materialism. People who oppose the Turing test say that the Turing test is useless because it only tests behavior, while what really makes a person a person is some magic inside them. John Searle says we can deduce via thought experiment that humans must have some "consciousness stuff" inside them, a type of matter that makes them conscious by its physical composition, that is conscious the way water is wet. At a lecture of his, I tried to get him to answer the question of what he would say if a computer passed the Turing test, but he dodged the question. To be consistent with his writings (which is not entirely possible, as they are not internally consistent) he would have to say that passing the Turing test means nothing at all, since his Chinese room posits a computer that passes the Turing test yet is "not intelligent".

Getting someone to accept the Turing test as a test of intelligence is a sneaky way of getting them to accept it as a test for consciousness / personhood. It's especially sneaky because failing the Turing test is not really their final objection to the claim that a computer can be conscious, but people will commit themselves to "Computers can't pass the Turing test" because they believe it. After computers pass the Turing test, it will be harder for people who made a big deal out of the Turing test to admit that they don't care whether a computer passed it or not, they still want to keep it as their slave.