Sure, back in the "day" many police officers had to buy their own guns. We used to check out our fixed sight guns with a variety of loads, both factory and handloaded. We bought and/or traded a lot of M&Ps trying to find one that was "perfect."
Never saw a Smith M&P, or Model 10 that didn't shoot almost exactly to POA with 158 grain lead Remington or Winchester standard old timey police loads.
Colt OPs did the same.
But, we were in the "modern" era back then. We had the new Super-Vels and Normas. And they didn't shoot to POA with ANY of the guns we tested. None of them did.
As to the "windage" difference, that's pretty common. With rifles, I can load everything exactly the same, except for the brand of brass and one will shoot to POA, while the other shoots left or right.
The only solution we knew of for using the new, faster 38s, was adjustable sight revolvers. So, I got a S&W Model 19-3 in, IIRC, November of 1970. I'd had, at an earlier time, a 6" Highway Patrolman, but had relegated that to Bullseye Competition because of the weight.
The blades on those adjustable sighted revolvers took a lot of abuse, hitting door jams, bumping various things. I just got mine out and noticed how I'd "rounded" the square edges on the outside of the sight blades to eliminate the various dings caused by carry in those Hume Jordan holsters.
With the Model 36s/37s, we just learned to live with the difference in height and found a load that shot at least in line with the sight (not left or right).
Again, back then, we often used the hollow based wadcutter with 5 gr. of Red Dot that Skeeter told us about. It shot pretty close in my snubbies.
As a Detective in '73, I found the newest model of Police Positive, 4", to shoot pretty close with the Norma 110 gr. hollowpoints so that worked for me.
When I went back to Patrol as a uniformed Sergeant in '74 I carried the Bianchi Judge holster that protected the sights.
But, I always wanted a Smith fixed sight for carry that would shoot those "hot' loads to POA. Never found one.
Bob