Have you ever seen it ON?
For a couple of months after purchase of 1080Ti (which I had got shipped from US), I was unaware of the fact that the fan was in a non-working condition out of the box. I too was under the impression that the fan would kick in only if the GPU felt the need, so never checked it.
On testing after a couple of months, found that the fan would not trigger in any condition, and the GPU would trip if temperature exceeded 90C. Getting it replaced would have cost me 1/6th to 1/5th the price of the GPU due to shipping and customs duty (I had to bear the cost of sending it to them and paying the octroi on return - this is EVGA Taiwan).
As a hack, I opened up the top acrylic cover to expose the internal heat sinks. Then set up an arrangement of 3 fans (2 blowers and 1 exhaust) for cooling. Looks badass now.