Right-handed shooter, right? Low/left issues aren't exactly uncommon for right-handed shooters. I've observed that it's generally related to a bit of recoil anticipation, loss of sight picture at the instant of firing (no follow through) and a bit of trigger jerk (or clenching the finger, 'curling' the finger and moving the trigger, and hence the gun, a bit leftward, especially when focus on the sight picture is lost at the instant of firing).
Granted, I had to make a very slight windage adjustment on my M&P 45. I didn't do it until I'd fired a few hundred rounds through my M&P 45 and had become acclimatized to the grip, balance and trigger, though. I don't make sight adjustments quickly or as a routine matter, either.
I can't count the number of times I've had someone bring me their duty gun claiming the sights were 'off' and that it wasn't accurate. More often then not, when I introduced an empty chamber condition or dummy round without their realizing it, they had the opportunity to experience their anticipatory flinch and/or trigger clench/jerk. Once they could actually feel it for themselves, without recoil occurring at the same time and masking it, they finally seemed to accept the possibility that it was happening because of something they were doing. That's the first step toward changing the software which is causing the hardware to act so that the condition occurs.
Holding the sight picture/alignment and following through with it for each trigger press helped a lot of folks over the years (myself included), instead of thinking about the recoil and preparing to 'handle it'. The gun can generally take care of the recoil as long as the shooter has a proper grip.
Learning to discount feeling the recoil and concentrating on the sights, trigger press and follow through ... especially under the watchful eye of a safety minded, more experienced shooter or instructor ... can be helpful.
FWIW, while working with a relatively new firearms instructor in recent years, and helping him with his personal shooting technique, I finally relented to adjusting his sights at his insistence. I told him that his grip, trigger press and follow through were the primary cause of his POA/POI issues, but he was insistent on having his sights adjusted. (His gun shot perfectly well when it came to POA/POI in my hands and the hands of another instructor). I told him he really needed to work on the software instead of modifying the hardware, but I made the change. He was happy with the results ...
Until his POI shifted the other way relative to his POA many weeks later, after continued work on his grip, trigger press and follow through. The trigger press and follow through were the major issues influencing his 'accuracy'.
Then, of course, I had to move the sights back to where they had been in the first place.
Another thing I noticed with my M&P 45 is that a couple of differences between the medium and small grip inserts wasn't immediately apparent. I liked the way the small insert felt on the gun in my hands. It made it feel very similar to a 1911 with a flat mainspring housing. The medium insert felt just a bit bulkier and 'less 1911-ish'.
On the other hand, the medium insert allowed me to make faster, consistently more tightly grouped shot strings, especially when involved in various drills (other than simply 'target' shooting).
In other words, the medium insert actually seemed to 'work better' during live fire than the small insert, even though the small insert felt better in the hand just holding it and doing presentations. Interesting. I didn't reach the decision of which to actually keep on the gun for a while, not wanting to have just one or two 'good days' at the range unduly influence me.
Don't get me wrong. The small insert gave me great practical accuracy, even at longer handgun distances (50+ yds), but the medium insert made it a better choice, for me, over the course of several months.
I did much the same thing with the medium & small inserts on the 99 series, too, eventually settling on the medium insert even though the small insert felt 'better' in my hand. The 'proof' was in the better consistent range performance, though, during live-fire spread over many range sessions and a lot of different courses-of-fire.
My M&P 45 has demonstrated itself to be very accurate. Surprisingly so. I can 'follow the hole' and make fairly tight cloverleafs at 15 yards using duty-type ammunition. One day, until I lost my focus,
I was able to shoot a 4-shot group that I could pretty much cover with the palm of my hand at 50 yards one day, standing, 2-handed unsupported.
It makes me wish I was a better shooter, that's for sure.
Just my thoughts.