We have Engine-Out Standard Instrument Departures (EOSIDS) for
EVERY runway at
EVERY airport that we operate from. That's every runway without exception
I'm sure of that because I'm the person who produces them, and have had written into the AOC "Operations are forbidden from Runways from which there are no published OESIDs". I sleep better that way.
There are numerous runways for which there are no significant obstacles for a straight-ahead track following engine failure, BUT, after acquiring MAA, cleaned up, and reduced to MCT, then what? Turn-back to the departure airport, or diverting to alternate inevitabely means encountering some of
John_T's rocky bits, so, all OEISIDs I produce provide lateral tracking and vertical obstacle clearance contained within 25 nm, assuring FAR 25 obstacle clearance until the MSA is reached. Inevitably, as 2nd and 3rd segment distances often exceed 30+ miles, the procedure enters a holding patter for further climb to MSA.
In doing it this way, every pilot using the procedures have a guarantee of obstacle clearance for every runway, all the way thrrough to where MSA is reached, and normal (PANS-OPS) clearance is assured. That's why I sleep better at nights.
To answer another aspect of the questions raised, for each procedure developed, I do not allow it's release until after a personal visit to the local ATC units to provide them with the "this is what we're going to do following engine failure" procedures. Usually, they're fairly surprised by the visit. In this way, neither the pilots, nor ATC are guessing "what next?" after engine failure.
For those who do know me, and know my regular flying job, I don't have the luxury of such complete assurance in my day to day flying. I do the work for one of our subsidiaries (we have 3). (No
Mutt, our procedures out of Hong Kong don't require continued flight to the Philippines, but the cr@ppy procedures we're stuck with in THAT operation might imply so

)
That's the way that one operator does it.
Best Regards, Nice to be back,
Old Smokey