In most instances, ATC will NOT specify a DP. Executing the DP procedure,
at least for Part 91 flights, is pilot option. There is no requirement to
notify ATC.

SMO lies in critical airspace. There is no way SoCal is going to launch
an IFR departure without very specific instructions.

It is so critical that a few years ago a Kingair elected to
circle-to-land Runway 3 after the tower was closed and they ended up
with a loss of separation with an air carrier departure out of LAX that
had been turned northwest over the ocean but too close to SMO.