Increasing speed does increase lethality if you have enough of an increase, but in handguns "enough" is not always available.
A 125 to 130 grain 9MM can be shot at about 1200 (give or take,) from a pistol barrel Thinking that going 1250 or 1270 is going to make any real world difference is not realistic.
Now if you were to slim it down to about 7MM and fire it at 3150 FPS you'd really see some difference, but that is called a 270 Winchester ----fired from a 24 inch rifle barrel.
So can a "smaller" caliber you can see huge differences in the lethal effects of a give weight of bullet, but the increase is usually measured in many hundreds of FPS and sometime thousands of FPS.