Good afternoon all.
The subject of all engine climb has not been covered all that well by manufacturers, regulators, or operators. We tend to focus on the engine out case because it is a certification requirement and our regulators demand it. There is a long standing belief that climbing safely away on one is a guarantee of SID compliance. Not true.
First off, we need to separate the apples from the oranges. The criteria for dealing with an engine failure are based on net takeoff fight path, 35 feet (dry runway) vertical separation and as little as 300 feet (or a splay, depending on where you are) laterally. This is also flown at relatively low speeds and the acceleration height is raised as required to ensure clearance (to a point of course).
Compare this to the standard instrument departure design. Basic obstacle identification surface, (152'nm) even over flat terrain, increased by 48 feet per nautical mile, all the way up to minimum enroute/safe altitudes (terms vary by document). Lateral splay is much, much wider than used for the engine out procedure. Aircraft flying a SID are operating at higher speeds and may accelerate relatively low, depending on noise abatement or other SOPs. Accelerating early is encouraged for fuel burn, but the lower you do it, the flatter the line from the departure end of the runway through the point you are climbing enroute.
Of course, further dividing the issue is the fact that an operator may have a specific engine out route established for a runway end. If this differs from the SID routing, does the operator conduct a separate analysis for the normal departure? None that I have worked with do.
Consider that more and more SIDs have high gradients not tied to terrain (ridiculously so, the last time I saw FRA at over 700'/nm). An engine out analysis based on terrain clearance may put you well below the SID. Consider three and four engine aircraft that may be more limited by the all engine takeoff distance than the engine out to 35 foot case, and you can start to see the delta. I have done some analyses of these cases and found all engine performance as much as 300'/nm too low for the SID. Yet pilots accept the clearance as they lack the information to do otherwise.
All this to say, you raised an excellent question here, but it is Pandora's box as the data to fully comply is simply not there for many aircraft types. Most operators would take a payload hit if truth were known, so don't look for this to get regulated any better.
Cheers
Vs