I love the hammer!
Want the best trigger for groups on paper? Cock it back for single action shots. Carry or have ready with the hammer down, for a deliberate pull of the trigger in order to make it go bang in a Self Defense situation. Theoretically, the heat of the moment might not be compatible with a hair trigger, but the accuracy you suffer from the long hard DA trigger pull won't likely make a difference in the close up ranges typical of SD encounters. Another theoretical SD heat of the moment concern (say in the case of a Beretta 92 or Canik hammered fired gun) is: Does the safety engage when the hammer is down? This means you pull the trigger and nothing happens. The safety is another manipulation required. I like that the CZ hammer fired guns (non-omega?) don't allow for safety engagement when hammer down in DA mode. Use the safety if carrying in SA mode with that hair trigger!
I have one striker fired handgun for SD purposes (Beretta NANO) and it features a horribly long hard DA-Revolver Like trigger that I LOVE for this purpose. No, it is not intended to shoot tight groups like a full size SA gun -- but if you practice with follow through, it performs quite well indeed!
A somewhat worrisome trend with Striker-fired handguns is the desire to include target pistol quality for them, in other words lightening up the trigger pull to near- SA hammer performance. There is always a trade-off. Will the hair trigger likely to "go off" with poor trigger finger control (or a jacket's rip cord that gets captured into the trigger guard)? To combat this possibility, some of these guns are "featuring" a manual safety -- something else to think about during the stress of a SD encounter.
The striker fired gun with no safety ala Glock is just easy to use and make it go bang. That IMO is the main attraction -- even the least intelligent among us can make it work. That, and the trigger pull is the same for every shot.
Proper training and experience will nullify all of the concerns above, but reality dictates that there will be many only-casual users of these firearm tools, so like cutting off a finger with a table saw, negligence happens.