The DA/SA trigger as found on many pistols serves no purpose. It is an answer in search of a question. Adding to the complexity of the firing system of any firearm is a bad idea. The fact that the DA/SA firing system is not found on any long gun proves the point. A firearm can only be rendered completely safe by rendering it inoperable, so there is no safety issue that the DA/SA firing system addresses. If you experience a misfire, that is not addressed by a DA/SA firing system. The fastest way to address a misfire is to cycle the action, which ejects the dud and chambers a fresh round, rather than pulling the trigger DA only to drop the hammer for a second time on the same failed primer, with predictable results. A DA revolver brings a fresh cartridge into play with each pull of the trigger, but no other type of firearm action does this.
As for the DA/SA pistol, I'm not sure why this firing system has become as popular as it is, as it makes the most difficult firearm to master even more difficult. But it is no surprise to me why 1911 style pistols are as popular as they are.