You're correct, with regard to terminal effect. 1/7 handgun incidents prove fatal, but most end somewhere between "missed the CNS, but hit" and "bleed to death". With the stated goal of stopping a threat as quickly as possible, as opposed to killing the threat, round selection does come into play a little more.
Ultimately, we need our round to be capable of stopping the threat...
A) through terminal effect (worst case)
B) by sending a clear signal to the brain that the body has been damaged
"Equipment" is certainly not as important as mindset, training, or skill, but it is still a worthwhile consideration. If it weren't, we would be sending our troops into the field with better training, funded with the money saved by arming them with single shot .22 rifles.
Currently Own: Beretta PX4 9mm, Glock 23 (Gen 4), Glock 19 (Gen 4) x2