Sights are for precision shooting.
As you noted, those sights aren't really good for that.
I am REALLY good friends with Ashley Emerson, the guy who came up with the Big Dot sight concept for pistols.
You have to understand the background to understand the mistake.
1. Ashley was starting from a premise that you "needed" to see the front sight before you pulled the trigger. This is a typical place to start from given the background and era in question.
2. Ashley knows more about optics and sighting systems than any other human I know. Because of this he knew that one group of guys that needed to see sights REALLY QUICKLY were dangerous big game hunters in Africa. He also knew that on their large bore double rifles, they often used large (ivory, traditionally) beads as a front sight. These beads could be picked up quickly and showed up well against the background of large dark beasts.
Now, on a rifle, you have 4 points of contact... 2 hands, body/shoulder and cheek. 4 points of contact are significantly more consistent than than the glorified 1 point of contact that you get from two hands on a pistol. This is important, because the rear sight wasn't very important to the close range hunting rifle application. The consistency of a proper mount and cheek-weld gets you "close enough" to align your eye in the "right place" behind the bead (which is 20-30 inches away) and give you enough field accuracy to hit the big beasties.
No such luck with a pistol. You NEED the rear sight to verify alignment of the pistol, which is held far away from the eye at extension. The relative difference between the front and rear sight in terms of distance from the eye isn't that great (20% increase at most for any defensive pistol) so they are somewhat close to the same focal plane (this is the reason that ghost ring sights on pistols don't "ghost" and suck, but that is whole different rant...). Because of this, the front sight needs to be significantly smaller than the opening in the rear sight in order to be "aligned" in a distinct manner.
The big dot gives you a really big front sight (go back to #1) which you cannot use for precision shooting because there isn't enough room on the gun to put a rear sight that is large enough to give you the ability to distinguish the front sight's alignment at a fine enough detail*. It was a flawed premise that yielded a product that was only successful because a large majority of the public bought into the flawed premise. Think of the big dot as the equivalent of fake relics from the holy land during the crusades. If you believe that you will be blessed forever because you have a magic splinter, you are likely to buy magic splinters if someone will sell them to you. (side note: if the guy selling the splinters really believe that they are magic, then you can't really be mad at him!)
Fast forward to the current Raison d'ĂȘtre for the big dot: "My eyes don't work as well as they used to, so I need a bigger/brighter front sight". On this point, I will concede that the underlying premise is at least valid. But let's return to the opening sentence in this response: Sights are for precision shooting. "Bigger and Brighter" doesn't have to mean "so big that I can't use the sights to shoot as precisely as I am capable of as efficiently as I can". The fact is that I have many students experience the fact that the big dot can very well cover up more than a 3" circle at defensive shooting distances. This means that it is physically harder to use the sight to place a round into that circle (some would say "impossible to do reliably", but that is an exaggeration. You can look for the top edge of the circle, then kentucky-windage your way a little higher... hold real steady... and place rounds consistently into targets smaller than the portion of your field of view that is obstructed by the front sight). The process for being PRECISE with a big dot is less efficient (ie- takes more time, effort and energy) than using a traditional blade & notch sight. If you really can't see any slightly bigger and much brighter front sight (there are plenty of options), then you have to admit that you probably can't be very precise under combative conditions, in which case putting a Big Dot on your pistol may be fine.
That is the long version.
The short version first articulated itself late one night around a campfire on a hunting trip with Ashley and friends in northern Colorado in 2004 or 2005:
Ashley: "So, c'mon, Rob, what do you really think of my sights?"
Rob: "Really?"
Ashley: "Yeah, I wanna know..."
Rob: "They're distracting."
Now, when you tell the guy who starts with the premise of "you must see the sight before you pull the trigger" that they are "distracting" you get a lot of "does not compute" and hilarity ensues... and we got a built in punch line that still comes up most of the time that we get together.
-RJP
* that point about not being able to get a "large enough" rear sight may NOT be true... it's just that I haven't seen a Big Dot placed inside a really wide traditional type rear notch side... as you can see in Badger's picture, you probably could fit a wide enough rear sight if you tried. Of course, then you probably would want a true BLADE that happened to be as wide as the Big Dot, because the straight edges of the Blade would be easier to be precise with than the round edges of the Dot. The width of the rear sight would be dictated by the width of the front sight, which would be dictated by the vision issues of the shooter... the smaller the better for more precision... which is what sights are for.