I have always thought the limitation was there to control track deviations at low altitude.
Not to my knowledge. It is presumed that the pilot can manipulate with a reasonable modicum of skill so track locus is reasonably well controlled. The track splay is intended to take care of minor tracking errors.
Also a wing down on a transport size aircraft will reduce your obstacle clearance by 20-30 feet, depending on span and bank angle.
If you scale, say, B707/DC8 at 15 degrees, you will find that the loss is around 15 ft .. hence the 35/50 delta for straight/turning departures.