Actually, for practical reasons. To save time. To find the optimum of time usage, depth, benefit and reliability. And because a mistake at the root would be much more severe than further ahead (as has been pointed out several times), we would need a delta shape anyway. The more I think about it: What we are talking about is practically identical to the DPA feature in the Fritz GUI....

Actually, I think the main reasons that we want a randomizer that changes the eval window with depth have to do with the fact that there is already far too much garbage in the results of the current randomizer.  Since it's true that it is more likely for one side to be able to avoid a position that is misevaluated by 0.5 units that is six moves away than one that is two moves away, it is more likely that the results six moves away are going to be completely garbage.  In the initial position, however, the opportunity for misevalation is at its highest, and the randomizer has the potential of remedying that if one can obtain enough non-garbage games to give a good sample size.  This is what one does by reducing the window after a few ply.

A second major issue is that the nature of the game can change after tactical possibilities.  In many positions, there are definite tactical possibilities that result in long-range strategical possibilities that are misevaluated by engines.  In tactical positions, one wants to have a high eval window, but in strategical positions, one needs a relatively low eval window because there are more moves available within such and such window, but if the window is still the same as in the tactical case, the vast majority of positions will be bad one way or the other due to an accumulation of inaccurate moves, and one has wasted a lot of time on those positions when the time would have been better spent looking at future ply to get a deeper tree.