If you have done E6 processing, you may have noticed that push processing will reduce DMAX and pull processing will increase it. (For example, this old Velvia50 I mentioned, pushed experimentally to 200, showed a very poor unusable magenta DMAX.)

This is because when developing for a shorter time in FD, less silver is developed in the (foggy) shadows, and thus, more dye is formed there in color developer after reversal. This is same for expired negative material; shorter development (pulling) also decreases fog. But for reversal material, this is more important way to fight against fog as you cannot "print through the fog" like with negatives, but the fog can spoil your blacks when projecting.

So, the reason itself is the pull process. Overexposing is then "needed" to get it into right density.

You are right that overexposure + pull process decreases contrast (as measured from the middle of the curve) but it may still be better to stretch the curve to give higher DMAX... Pull process increases the density range, which is different thing than contrast.

I hope I got it right.