Why would you need a procedure to avoid obstacles when you are avoiding obstacles visually?? You follow the engine out terrain clearance procedure if IFR, If you are not you follow it anyway or look out the window and choose a better option visually.
Let's get practical, from a B737 point of view. I flew loan contract, for a summer season, for an European airline in 80's before their XAA imposed RTOW tables. They used QRH performance tables for thrust & speeds = balanced field. They used visual avoidance techniques. My host airline had RTOW tables & emergency turns. It raised my eyebrows somewhat, and confused me. A year later their 'local XAA' imposed the same sort of rules as my host airline.
I was curious how a visual avoidance manoeuvre was executed. As the nose rises through 10 degrees attitude the horizon, over the nose, is invisible. The rotation continues until 15 degrees and earth beneath and in front of you disappears. How can you visually avoid something you can not see? No answer.
Other a/c types might have shallower climb out angles, but not any major jet airliner I've seen or flown.