Ah, you've discovered the truth about "DAO" striker-fired guns - they are not DAO guns.
A true DA trigger both cocks the action and releases the trigger. The action on an M&P is 98% cocked by the slide leaving a miniscule 2% left for the trigger - something that is indistinguishable for the shooter. In fact, S&W literature talks about how they developed the M&P to mimic an SA trigger.
And quite frankly, they did a pretty good job of it. My M&P 40L has a drop-in Apex trigger kit that results in a 2.7# trigger - a full pound lighter than either of my far more expensive 1911's. Sure, nothing will make the M&P trigger as slick as a good 1911 trigger, but these allegedly DAO guns are routinely beating the 1911s in competition. They are that fast.
Too fast for defensive use IMHO.
If you are facing down a bad guy and have your gun drawn and pointed at him, then rest assured that the safety is off and your finger is on the trigger.
But, that does not mean that the decision has been made to shoot him. Not yet. If you're lucky he'll turn and run like crazy and you managed to NOT press the trigger enough to make the gun fire, then the scenario ended without having to shoot anyone.
OTOH, if your finger pressed the trigger just a tad too much because you had gallons of adrenalin pumping through the veins & your fine motor skills went south and you shot the guy as he was turning and running - well, that was a very bad day for both him and you.
I prefer DA/SA or
true DAO guns for defensive use. I want a relatively long and heavy trigger pull on the first shot because I know that half the brain goes out the window in a real deal scenario as well as all wonderful fine motor skills we finesse our target and competition triggers with. That usually means starting out with a brand new 10# DA trigger that will turn into a lovely 7# trigger after action work. Perfect for defensive use.
We have owned several M&Ps and my M&P 40L is my favorite competition pistol. Our first was a 9c that I bought for concealed carry. That didn't last very long once I realized how easy it was to deploy the trigger. While not as nice as a 1911 trigger, the stock M&P trigger is just about as easy to pull as a basic 1911 trigger. In fact, S&W says that they developed the M&P to mimic an SAO trigger. As a result, the M&P trigger is far easier to deploy than on any of our Sig's, S&W 3913's or Kahr's. So, I carry Kahr's when I want small and light, Sig's when I want more capacity and the 3913 when I can't make up my mind.

BTW, I do have a very nice 1911 for carry, but it isn't my favorite because it is simply too darn fast on the first shot, and not one bit faster on the second than my Sig; probably slower.
Do no harm.
Wyatt Earp said
"Draw fast, shoot slow." That's easier to do when the gun is designed with that in mind.
Our solution was to sell my M&P 9c carry pistol and replace it with Sig P226 & P6 for home defense and Kahr K9/PM40/CM9 for carry. We've just recently augmented/replaced the Kahr's with a pair of S&W 3913's with true DA/SA triggers.