aeroncaman
As pilots we must have that information so that we know whether we can stay with the SID or need to take up the emergency turn/contingency procedure.
It either needs to come from the manuals (which it has done in the aircraft I have flown), or be provided in the form of performance analyses from commercial companies or airline performance planning departments.
Mostly agree, however...
Pilots do not have all of the obstacle data required to perform their own analyses.
For example SID gradients do not include consideration of low, close-in obstacles which may become very significant in OEI situations.
The notes accompanying the COWBY4 contain a listing of groups of obstacles, but these are not specified with sufficient precision for a pilot to make her/his own calculations.
As you say, the pilot MUST know whether or not it is possible to remain on the SID, but the answer has to come from a performance engineering entity that has access to the requisite obstacle surveys.