I'm not sure you really know what you're looking at.
The DAK is not really that "new". It's a system that is a double action only system with a twist. It adds a second reset point. Think of it this way: if you use a long crowbar/lever to lift something, it takes a lot of travel to accomplish, but not a lot of force. If you shorten the lever, the distance required is shortened, but the force required is increases. Basically the same thing with DAK. If you let the trigger out all the way after each shot, it's a long, but relatively light DA pull. If you only let the trigger reset to the first position, you have a heavier but shorter pull. This is kind of the opposite of the traditional DA/SA, where the first shot is a long, relatively heavy double action pull, but the action of the slide cycling cocks the hammer for follow up SA shots that are light trigger pulls. Because I'm not sure you know, a double-action pull does 2 actions: pulls the hammer back and releases it. In single action, the hammer is already cocked and the pull just releases it.
I have never had anyone really explain logically why the DAK is desirable other than reducing the likelihood of an unintentional double-tap. Was there really a problem of people meaning to shoot someone just once, but accidentally keep shooting them?
You raised a concern that if you don't let out the trigger far enough, the pistol won't fire. Well that's going to happen with any pistol that's not fully automatic. There are pistols that have shorter resets than most (PPQ, SIGs with SRT), some that are very distinct and some that are mushy. I've heard of no complaints of false resets with the DAK. As for legality of owning, I know of no jurisdictions that outlaw the DAK system.
It sounds to me like you're pretty new to firearms. I suggest you learn more about how firearms work and take a class or two from a reputable instructor. Rent a lot of pistols before you decide to purchase so you get a feel for the different actions, controls, ergos, etc. A lot of people have had bad experiences buying firearms because some cool federal agency uses them or they saw it in a movie or just think it looks cool.