Avoids edge cases where the randomly selected curve was broken or an outlier.
More importantly, theoretically, we would like to minimise variance, particularly variance caused by assuming the intercept should be at the position of the smallest split threshold.
Variance is calculated by distance from the mean, so why not find the mean, and offset everything to minimise distance to that mean.
Using a random curve, and moving everything to that curve, does mostly that, but not as strongly.
I suspect that it creates a new mean curve near to the target curve, and most curves are now near that mean.