Well, if you increase velocity you will increase the energy, which makes it more powerful. More power will increase penetration and cause more damage, so it stands to reason it could stop the fight faster. You go out and shoot a deer with a 9mm pistol, and then shoot one with a 357 and see which one runs further and takes longer to die.
As others pointed out, it gets more complicated than that. The metallurgy of current projectiles, along with, how jackets are tapered, how pre-scored jackets are cut, jacket bonding, etc, are all done to get projectiles to achieve reliable expansion and penetration levels within a certain velocity range.
Firing a 115 grain 9mm bullet at 1000-1100 FPS may get the bullet to expand to maximum expansion range without fragmenting, in order to still hit ideal penetration of 12-18” in calibrated gel (I know, “Bad guys aren’t made of gel. However, this medium allows repeatable testing for comparison of bullet performance to evaluate design.)
Drive that same bullet to 1200-1300 FPS and it will indeed deliver more energy. This may come at the expense of early, violent expansion or even fragmentation. This can reduce penetration, and prevent a projectile from reliably getting to vital organs.
Other bullets may have a broader velocity threshold. A 124 or 147 gr may have enough residual weight, projectile length (which contributes to sectional density and increases penetration capability) to still hit required penetration depths.
FBI data collected for decades tends to point to that penetration depth range as being one of the more critical factors in getting more rapid stops from increased bleeding. Reliability and shot placement are still most important.
For me, I’ll take standard pressure loads that I can hit well with and with a round that has a record of hitting ideal penetration depths, and reliable expansion.
124 and 147gr Federal HST, or Speer Gold Dots are what I try to keep stocked up on for carry.
My carry pistols tend to have barrel lengths that don’t tend to take advantage of +P loads anyway.