South Coast , you are indeed correct. But the issue is not necessarily the SID limitations, one's will find that the most restrictive obstacle are very often close-in obstacles and not the second segment as per say.
As a consequence a proper runway analysis is always preferable.
If someone like to have a good video i can recommend this one
even if it is applying to OPS-Specs and Terps, it remains totally valid for PANS-OPS and EASA ( with different numbers); in terms of assessments