Thank you
We don't have national rules about this. It seems logical to me and also convenient to have standard international rules. Otherwise it would be a mess, since pilots and airlines come from everywhere.
I have some knowledge of nearby obstacles, but that doesn't allow me to provide such instructions, because I cannot guarantee, for example, that ground proximity warnings will not be triggered in the cockpit, nor do I know navigation tolerance errors in the instruments of the aircraft, or required minimum rates of climb to clear the obstacles (what would happen in the event of engine failure, for example?), etc.
And you say that If I authorize a SID deviation requested by the pilot below minima I am not vectoring the aircraft nor providing a direct route, but what is the difference? I am authorizing a turn to some heading or some point below minimum safe altitude. The pilot is just asking for such clearance. It doesn't really matter who is the first to propose it, because in the end, it has to be approved by the ATC.