They are great for distances you don't need sights for. They suck for anything else. Note zero serious competition shooters use them, and competition is where hundredths of a second matter. If there was a speed advantage, you'd see them there. I am unaware of any police or military unit using them, which again is probably a clue.
Depending on what you're looking for, I'd take a look at Trijicon HDs, Warren Tactical, or Ameriglo CAP.
Trijicon HD Vs factory Sig Sights, I noted a small but noticeable gain in sight acquisition speed on the timer, and also noted the front sight was easier to track under recoil. In something like the FAST test, maybe .15 seconds total gain.
I agree to an extent. In competition we are generally using fiber-optics, which I feel are too fragile for and EDC gun, so going the other way those sights wouldn't translate well in the defensive pistol world the same way the Big Dots wouldn't be great for competition. Accuracy is what kills the Big Dots for any competition role, which you rightly pointed out.