They've acknowledged the demand... (Destiny)

by Korny , Dalton, Ga. US. Earth, Sol System, Thursday, March 26, 2015, 18:12 (3778 days ago) @ Xenos

http://blog.us.playstation.com/2015/03/25/ps4-system-update-2-50-available-tomorrow-features-detailed/

I can now try what I wanted to do back in November:

• L3 -> Red Circle (Crouch)
  
• R3 -> L3 (Sprint)
  
• Red Circle -> R3 (inspect player)

Bad news is that it screws up menu control since Red Circle is the standard 'back' button, so I might settle for swapping the sticks. But combat and running around definitely feels smoother :D

Do we have any idea if you can assign different control schemes to different games/apps, or is it system-wide.

They said that at launch it would be system-wide, but that they'll look into allowing you to assign it to specific games/apps. Can't look up source at the moment, but it was in the PSblog article where they announced control-mapping. Comments section.