Port,
Using the TITAN1 as an example: fly heading 045 to intercept the BNA068 VOR radial.
We would expect you to fly heading 045 until you intercept the VOR radial (BNA068R). If we have to hold a subsequent departure until you are far enough from the airport or above an altitude then that is what we have to do.
Some SID's are established for noise abatement procedures so by making a sharper turn, or an early turn would take you off the noise abatement track, which could generate unwanted phone calls.
Mike