Ah you see, you just essentially moved unique constraint to a client. It is no different generating an ID on client side and making a request. It is not idempotency.
Idempotency-Key should not replay the response (it depends, actually). But also it should not error 409. You need to be content aware before adding Idemmpotency Key header handling.
What will happen when the request is received and handled but during writing response body TCP connection dropped unexpectedly. And after second or two a connection reestablished. How two sides agree that previous request accepted and everything good to go? That's what Idempotency-Key header does.
Idempotency-Key should not replay the response (it depends, actually). But also it should not error 409. You need to be content aware before adding Idemmpotency Key header handling.
What will happen when the request is received and handled but during writing response body TCP connection dropped unexpectedly. And after second or two a connection reestablished. How two sides agree that previous request accepted and everything good to go? That's what Idempotency-Key header does.