Speed factor is pretty important, actually. I used it in my years of game mastering, ages ago in the first edition era.
The way it works is at the beginning of every melee round, all combatants roll a ten sided die, add their weapon's speed factor to the roll, and then add/subtract any dexterity modifications to the sum. The lowest numbers go first. And, as Mal said, it's often possible for characters with the lower initiative to kill or otherwise incapacitate a character with a higher initiative before he/she/it gets to attack, thus eliminating the attack altogether. It adds a firm element of realism to combat. Anyone who frequently watches boxing can tell you that it's not infrequent to see someone get knocked out in mid punch.
Heya, Mal, could you do me a huge favor? Go down to Lee's Hoagie House, buy me a jumbo cheesesteak with mushrooms and jalapenos, and mail it to me via Two-Minute Priority? That was my favorite resteraunt, but, unfortunately, I haven'y been there in about 12 years...