The most likely reason is to make the adjustment behave better both visually and tonally, especially at the extremes.

From the answers here, two factors are relevant:

1. Human brightness perception is not perfectly linear. A mathematically linear exposure shift does not always look visually natural, especially near black and near clipping. A non-linear curve can make the control feel more perceptually even.

2. Very dark sensor data may not behave ideally linearly. In the deepest shadows, capture and quantization can be less uniform, so a custom curve can help avoid harsh behavior, banding, or ugly shadow changes.

In practice, this means the exposure slider is designed to act mostly like a linear exposure change through the middle tones, while gently protecting shadows and highlights. The quadratic sections are likely there to smooth the transition near black and near the brightest tones so edits look more natural and are less destructive.

How important is it? Usually, the effect matters most in extreme shadows and highlights. In midtones, it will behave close to linear, so for many images the difference is subtle, but near the tonal limits it can noticeably improve the result.