The Turing Test isn’t really intended to identify a computer – Turing’s problem wasn’t that we needed a way to identify computers.

At the time – well, and to some extent today – some people firmly felt that a computer could actually think, that that is something “special” that only humans can do.

It’s intended to support Turing’s argument for a behavioral approach to thinking – that if a computer can behave indistinguishably from a human that we agree thinks, then that should be the bar for what we talk about when talking about thinking.

There have been people since who have aimed to actually work towards such chatbot, but for Turing, this was just a hypothetical to support his argument.

https://en.wikipedia.org/wiki/Turing_test

The test was introduced by Turing in his 1950 paper “Computing Machinery and Intelligence” while working at the University of Manchester.[5] It opens with the words: “I propose to consider the question, ‘Can machines think?’” Because “thinking” is difficult to define, Turing chooses to “replace the question by another, which is closely related to it and is expressed in relatively unambiguous words.”[6]

Turing did not intend for his idea to be used to test the intelligence of programs—he wanted to provide a clear and understandable example to aid in the discussion of the philosophy of artificial intelligence.[82] John McCarthy argues that we should not be surprised that a philosophical idea turns out to be useless for practical applications. He observes that the philosophy of AI is “unlikely to have any more effect on the practice of AI research than philosophy of science generally has on the practice of science.”[83][84]