The shape of the curve doesn't matter at all. What matters is having a mismatch between the capture curve and the display curve.

If you kept it linear all the way to the output pixels, it would look fine. You only have to go nonlinear because the screen expects nonlinear data. The screen expects this because it saves a few bits, which is nice but far from necessary.

To put it another way, it appears so dark because it isn't being "displayed directly". It's going directly out to the monitor, and the chip inside the monitor is distorting it.