Speaking from a pilots point of view I have done this quite often in gin clear weather at (usually secondary) airports where the SIDS have a rather extended routing for terrain separation. I understand SIDS are created with a rather shallow climb gradient and must avoid terrain by a fixed margin. My aircraft can outperform this by a factor of 10, I can see the mountain and therefore avoid hitting it, so the procedural separation isn't required.
at the other end of the flight we sometimes do the same thing on descent - vmc avoid terrain visually - and usually finish off with a visual approach, all while being on an IFR flight plan. I'm afraid I don't know off the top of my head if there are any ATC procedures published that relate to this in the countries where we do it.
I also heard from a friend working at a procedural airport that some pilots do it to reduce separation on diverging departures, but I guess it's no different to reporting #1 in sight and following visually, something else I try and do whenever allowed. In other places I fly the tower can separate visually allowing reduced departure separation or early turns.