When I draw the gun, as it rotates to horizontal over the holster, the safety goes off and I ride the safety. The two hands then meet and I have my combat ready grip with the gun ready. That is SOP that if I draw the gun, it is ready to fire until I decide otherwise. If I deptermine that I may not need to fire, I may engage the safety while remaining at scan position. Whenever searching, the gun is on safe. Regardless of circumstance, trigger finger stays off trigger until the decision to fire is made.
Having the safety come off as the gun goes to horizonatal is part of the draw sequence that many people don't follow and who often have a bowling ball draw or fishing pole draw. As the gun is raised from the holster, it is then rotated to horizontal over the holster. Off hand is at the center of the chest and is reaty to accept the gun and gun hand or to perform other tasks such as fending off blows, opening doors, etc. Many people fail to realize how important the off hand is. In this position, the gun can be fired at the opposition, albeit from the hip which may be necessary if the off hand is fending off the opposition. If the gun isn't fired, it can be kept trained on target as the gun and gun hand meet with the off hand at the center of the chest. The hands come together, grip is established, and arms extended as necessary. At any point in the draw once the gun is horizontal, it is ready to go.
This is contrary to some teaching I have received that went with the idea that the gun is always on safe until the need to fire. The idea of keeping it safed is to prevent accidents.